In-Floor Heating for a Shop & Greenhouse - Considerations ?

[not2old]

Just so happens the local building inspector is a good friend of mine and has been in my shop numerous times and has seen my dedicated HWH as well as my Calaffi distribution system and has never said boo crap about it. In fact he wanted the particulars as he's building a new pole structure and wanted to see how mine operates. Floor is presently running at 70 degrees, fully heated and the HWH basically idles 75% of the time.

Hard to beat a warm concrete slab IMO.

Do you know how many watts your HWH uses and how large is your shop? I'm trying to determine whether a HWH, waste oil boiler or geothermal water to water unit is best for my purposes. A 2000w HWH running at 25% calculates to less than $2.00 per day for 1600 square feet and I find that hard to trust. My climate here is likely slightly warmer than yours. I like the idea of using a HWH as there is no chance of freezing during a power outage if using glycol.

 

[Rustyiron]

....and there are propane and oil fired hwh's also depending on your electric rates or available panel capacity.

 

[dstig1]

You could calculate the BTUs needed, but it won't be easy. There are HVAC standards for this (I think it is called Manual J) that will take into account insulation, windows/doors (and how good they are), climate, sun, etc. Mine uses a tankless water heater that is modulating and rated for 11,000-190,000 BTUs. I can't really tell how much heat it is putting out other than when it first starts up it is much louder than what it settles down to after 15-20 sec. My guess based on that is on the low side of that range, but I really had no idea how much heat i would need and wanted to be safe. I'd say it was way overkill.

 

[quicksandfarmer]

I've installed a number of heated floors. Some things to be aware of when using it for your sole source of heat:

The amount of heat the floor puts into the space is directly proportional to the difference in temperature between the surface of the floor and the room. The rule of thumb is two BTU/hour per degree of difference. So if the room is at 70F and the floor is at 85F the floor is putting out 30 BTU/hour per square foot. If your floor is 1,000 square feet that's 30,000 BTU/hour.

One thing that follows from this is that in a high heating load building, you may not be able to get the floor hot enough to meet your heating need. The limit is how hot the floor can be and be comfortable, most people can't stand comfortably on something over about 90F for any length of time, some people get uncomfortable at even lower temperatures. If you need more than 40 BTU/hour/square foot you won't be able to achieve it solely with a heated floor.

If you have a high heating load, it's very important to keep the floor temperature constant. The above formula is based on average floor temperature. But if half the floor is at 100F and half is at 70F the hot part is too hot and the average may not be enough to meet your needs. Designing layouts is a whole subject, but briefly the way to keep the floor constant is to limit the length of coils, space the tubing fairly closely and run the tubing symmetrically.

With only floor heat, the only way to modulate how much heat your floor puts out is by modulating the floor temperature. This can be a problem. The limit to how quickly you can change output is how fast your floor can change temperature. Even on the shortest day of the year a building in the sun can absorb 20,000 BTU per hour from solar gain. If you've got a 30,000 BTU/hour heating load like in the example above, when the sun goes down you go from 10,000 BTU/hour to 30,000 BTU/hour pretty quickly. At 10,000 BTU/hour, that floor needs to be at 75F, at 30,000 BTU/hour it needs to be at 85F. A thousand square feet of concrete, 4" thick, weighs about 40,000 pounds. To change the temperature of 40,000 pounds of concrete by 10F takes about 200,000 BTU. If your heater is sized for 30,000 BTU/hour that's seven hours of continuous running to get the slab up to temperature. Then in the morning when the sun comes up you overheat until the slab cools down.

In residential applications the thinking has moved away from concrete floors to systems like WarmBoard, which someone linked to above. WarmBoard bills itself as "high responsiveness." It has a low heat capacity, which means it can change temperature quickly to respond to changes in heating load.

If you can't use a low heat capacity system, I recommend against using a heated floor as your sole source of heat. Instead, couple it with a system of some type that will allow you to quickly adjust the amount of heat being output. Size the floor so that you can have it at a nice temperature for the entire heating season -- I like around 78F. On the warmest heating days it can be your sole source of heat, on cold days or when you want to heat up in a hurry you supplement it.

If you only want to have one boiler for the building, you can use either baseboard radiators or fan convectors powered by the boiler when you need heat in a hurry. You could also have a separate forced air heater.

 

[LD1]

Do you know how many watts your HWH uses and how large is your shop? I'm trying to determine whether a HWH, waste oil boiler or geothermal water to water unit is best for my purposes. A 2000w HWH running at 25% calculates to less than $2.00 per day for 1600 square feet and I find that hard to trust. My climate here is likely slightly warmer than yours. I like the idea of using a HWH as there is no chance of freezing during a power outage if using glycol.

Im not a radiant floor expert. But the two people I know that have it in their slabs both use a lochinvar boiler.


Most electric HWH use 4500 or 5500w elements. A 5500w element running 25% of the time is 33kwh/day or about 1000kwh/mo. (my electric rates, that would translate to ~$150/mo for heat

 

[rScotty]

Do you know how many watts your HWH uses and how large is your shop? I'm trying to determine whether a HWH, waste oil boiler or geothermal water to water unit is best for my purposes. A 2000w HWH running at 25% calculates to less than $2.00 per day for 1600 square feet and I find that hard to trust. My climate here is likely slightly warmer than yours. I like the idea of using a HWH as there is no chance of freezing during a power outage if using glycol.

I wouldn't get to much involved with the heating BTU math. Unless you want to dive in pretty deeply the simple calculations just lead to the wrong conclusions about floor heat.

It's easy to know how many watts the HWH floor uses - as well of all the other factors. But ultimately it doesn't matter. That's because there are a couple a unique things about a heated floor that need consideration.

First thing to realize is that for a heated floor to be the primary source of winter heat for a room, that floor would have to be far too hot for comfort. That is why a boiler that reaches temperatures like a wood stove is not efficient for floor heat. Then because the heated floor conducts heat from deep inside the floor out to the surface of the slab very slowly, you cannot use the same heating emission and conductance considerations for the slab hat you do for floors, walls, and windows.

So having a boiler with the ability to quickly heat the hydronic fluid a lot hotter than you want the floor to become doesn't help heat the building. Instead of a that quick hot boiler, you will be better to use a source of inexpensive heat like a HWH and allowing it to set a baseline floor temperature - I use 60 degrees.
Then the house/shop will never freeze in the winter and, never be cold when you walk in after a vacation, and still be comfortable on warm days as well as cold. On days when the weather is warm enough to keep the floor at 60, zone thermostats simply turn the slab heat down or off. You can leave it on all summer....

That sort of heat - where a heated floor heat only sets the baseline room temperature - takes advantage of the strong points of having a heated floor. It is inexpensive and reliable. But it also means there is a necessity to add a faster acting source of high heat - like forced air or a wood stove or baseboard - to warm the air in the room and counteract the room wall & window BTU surface losses to the outside. But since the room already has a lot of mass maintaining a reasonable baseline temperature, the fast heat can be quite small. Don't go overboard there until you see what is needed.
Luck,
rScotty

 

[not2old]

I'd like to thank everyone for their input. I now realize that I needed to double my estimated power usage. This now gives me the confidence I need to proceed. $600.00 per heating season of about four months is totally acceptable to me. I expect to heat the floor to the point of keeping the air at 56*. I've done this in my garage and find that after working for 1/2 hour or so that I can remove the sweater and work comfortably in just a shirt. The electric HWH are free as our condo rentals require they be replaced every 10 years, leaking or not. I have 6 sitting there now. When I see the bills, I will decide whether or not to upgrade to something else. It will be next year before this happens as I'm now ready to install the wiring in the spring. Already anxious to see this working.
Never in a million years would I have guessed that a web site with a bunch of old farts with tractors would be my go-to for answers to everything.

 

[rScotty]

I'd like to thank everyone for their input. I now realize that I needed to double my estimated power usage. This now gives me the confidence I need to proceed. $600.00 per heating season of about four months is totally acceptable to me. I expect to heat the floor to the point of keeping the air at 56*. I've done this in my garage and find that after working for 1/2 hour or so that I can remove the sweater and work comfortably in just a shirt. The electric HWH are free as our condo rentals require they be replaced every 10 years, leaking or not. I have 6 sitting there now. When I see the bills, I will decide whether or not to upgrade to something else. It will be next year before this happens as I'm now ready to install the wiring in the spring. Already anxious to see this working.
Never in a million years would I have guessed that a web site with a bunch of old farts with tractors would be my go-to for answers to everything.

OK. with 6 water heaters available... Before you wire the shop, think about the possibilities. An electric HWH already has two heating elements which can be wired to come on alternately or at the same time.
HWHers aren't large and have to be stored anyway, so there should be room to plumb all those extra hot water heaters into your system. Using any and all combinations of parallel and series flow - I believe you could entertain yourself for hours figuring out wire sizes, heat storage, and watts.
rScotty

 

[quicksandfarmer]

You could calculate the BTUs needed, but it won't be easy. There are HVAC standards for this (I think it is called Manual J) that will take into account insulation, windows/doors (and how good they are), climate, sun, etc. Mine uses a tankless water heater that is modulating and rated for 11,000-190,000 BTUs. I can't really tell how much heat it is putting out other than when it first starts up it is much louder than what it settles down to after 15-20 sec. My guess based on that is on the low side of that range, but I really had no idea how much heat i would need and wanted to be safe. I'd say it was way overkill.

Manual J is correct. For cooling it's pretty involved, but for heating you an do a reasonable estimate on the back of an envelope.

There are only two heat losses you have to worry about -- through surfaces, and air leakage. Heat conducted through a surface is easy to estimate, the R-value that is used to rate insulation was created to make the math easy, one square foot of surface with an R-value of one will lose one BTU/hour with a temperature difference of one degree F. More generally, the heat loss through a surface, in BTU/hour, is the area in square feet times the temperature difference between the two sides divided by the R-value.

The first step is to figure out how cold it gets where you are. At this site: https://www.energystar.gov/ia/partn... Temperature Reference Guide - 2015-06-24.pdf

You can get county-level climate information. The "99% Heating Temperature" is what you use for system design. Once you have that you add up the area of all the surfaces in the building -- walls, ceiling, floor, doors and windows -- and calculate the heat loss for each one at the design temperature.

Here's a simple example:

Imagine a simple building, 1000 square feet, 25x40. Walls are 10' high, flat ceiling. It has 100 square feet of windows and 100 square feet of doors. Walls are insulated to R20, ceiling to R40, doors are R5 and windows are R3. Floor is concrete slab with 2" of foam, R8 total. Let's assume it's where I am, Newport County, where the design temperature is 9F. And I want to keep it at 70F. So the difference between inside and outside is 61F.

I have two walls that are 25x10, 250 SF each, 500 SF. I have two walls that are 40x10, 800SF. That's 1300 SF, take away 100SF of doors and 100SF of windows that's 1100 SF at R20. Total heat loss through walls is 1100*61/20=3355 BTU/hr.

Ceiling is 1000 SF at R40, heat loss is 1000*61/40= 1525 BTU/hr.

Doors are 100 SF at R5, heat loss is 100*61/5=1220 BTU/hr.

Windows re 100 SF at R3, heat loss is 100*61/3= 2033 BTU/hr.

With a slab floor the underside isn't going to be at outside temperature, more likely it will be near your year-round average temperature. A quick and dirty approximation is to average your heating design temperature and cooling design temperature. For me that's 85F, which gives a soil temperature of 47F, or 23F below interior. The floor is 1000 SF at R8, so that gives a loss of 1000*23/8= 2875 BTU/hr.

Add them all up and you get 11,008 BTU/hr.

For air leakage most of the time you'll do an educated guess. In new construction done to the latest codes you actually measure the building, but that's unlikely here. Let's say this building is pretty leaky, the air turns over every two hours. It has a volume of 10,000 cubic feet, so that's 5,000 cubic feet per hour or 83 CFM. Putting that into my calculator I get 5500 BTU/hr for the air leakage at 9F.

That gives a grand total of 16,500 BTU/hr.

I can help you do these calculations for your building. Without doing them, it's exceedingly unlikely that you'll end up with a system that works the way you want it to.

 

[quicksandfarmer]

To follow up on my hypothetical, a load of 16,500 BTU/hour in a 1,000 square foot building is 16.5 BTU/sf. To achieve that you'd need the floor temperature 8.25 degrees above room temperature; with an interior temperature of 70F you'd need a floor temperature of 78.25F.

But that's your maximum heating load. What about on an average day? Where I am, January is the coldest month, average daily high temperature is 39F and low temperature is 26F. If you've read what I wrote in #44, I don't recommend sizing for the coldest days, I actually think a floor should be sized for the high temperature on winter days and then supplemented.

If my heating load at 9F is 16,500 BTU/hr, at 39F it's going to be almost exactly half of that, about 8300 BTU/hr. So my recommendation would be to size the floor for that output and then have another 8300 BTU or even more of other heat. That way you an run the floor at a nice even temperature and kick on the heater when it's really cold out or you want to warm up in a hurry.

With a floor area of 1000 square feet, that's 8.3 BTU/sf, which means a floor temperature of just over 74F. Which won't be cold, but probably will be barely perceptibly warm. And you might find that kind of disappointing after all the trouble.

This raises an issue with heated floors: in well-insulated buildings you don't need as much heat as they put out. From a warm-and-cozy perspective they work best in poorly-insulated buildings.

In residential construction I recommend not doing them throughout the house, but instead only in strategic places -- bathrooms and maybe the den. That way you can run them warm without overheating the house.

But definitely do the math before laying any tubing.

 

[rScotty]

SNIP....
But definitely do the math before laying any tubing.

I agree with that. Math saves a lot of work. But floor heat can be different from traditional calcs.
When you start figuring how many BTU you need, give some thought toward the RATE at which heat moves in and out of different surfaces and through different materials. You can use math for rate of change calculations as well as for simpler sums. For floor heat, heat input can be very slow compared to outflow. That makes a difference, but the good news is that it will work even if you make a mistake. And is easy to change as long as there are enough loops of pipe in the floor to begin with. So err on the side of too many loops if you have any doubts.

Floor heat involves a lot of different surfaces and heat exchange steps. If doing it on the back of an envelope, I'd try to treat each transfer across a surface as a separate transaction, then estimate or calculate exchange rates as well as BTUs.

Do the math both ways, and think about the way that the "rate of heat transfer" will cause a floor heat system to differ from forced air heat calculations.

Another design difference to think about is that in floor heat systems, heat can be stored in a tank to be used later. That is something that is hard to do with warm air. HWH tanks are great for storing warm fluid.

And remember - no matter what you do, math is just a tool. Don't get hung up. Floor heat is great to have and will work in spite of mistakes in calculations. Floor heat is basically continuous parallel loops of warn fluid in and cold out - AND ANY AMOUNT OF BTU IS AN ADVANTAGE. All it takes is plumbing in two additonal valves to be able to accept heated fluid from any source. Doubling the input BTUs is simple.

A fist-sized silent Taco pump will drive fluid through several thousand feet of PEX tubing. In a low temperature type floor heat (the best kind) all the manifolding and valves can be standard plumbing fittings.

Most all the various ways to heat the fluid are safe, basic, and can be easiliy changed - so don't be afraid to experiment.
enjoy,
rScotty

 

[AnotherBueller]

As others have said with more words, concrete floors have a very slow heat transfer rate to objects in the room and anything on the floor will insulate that warm floor from the stuff in the room.
Concrete is VERY unresponsive to rapid temperature change.

 

[dstig1]

Quicksandfarmer - I am puzzled by your comments as both my house and shop are fully and only heated by hydronic radiant tubing. The shop is slab on grade and the house is basement slab, main level, and smaller upper level. The house is tubing in the slab and the main floor was engineered to hold 1.5" on concrete on top of the subfloor in which the tubing was placed. Another layer of subfloor was put on top of this on sleepers. The small upper level was done with staple-up. Both buildings are SIPs and tightly sealed and very well insulated. Outside Minneapolis. The shop has no issue heating from the floor and it is 2600 sf with 13' ceilings (R48 ceiling).

The house actually runs into problems in very cold subzero weather with not being able to keep up 100% so during long cold snaps I sometimes have to turn on the furnace to help out a bit. The furnace is mainly there for the AC in summer and is used in the fall and a bit in the spring to avoid turning on the floors during times of changing conditions. My issue appears to be the pressure drop in the on-demand heater creating too much back pressure to allow for high enough flow to get enough heat output. from the floors. I think I might have better luck with a tank HW supply, but I am fairly stuck at this point... I tried many things to increase the flow without great success.

 

[quicksandfarmer]

but the good news is that it will work even if you make a mistake. And is easy to change as long as there are enough loops of pipe in the floor to begin with.

There's basically three ways it doesn't work:
* In order to get enough output to heat the place the floor has to be so hot you can't walk on it; or
* The floor puts out so much heat that to keep the room at a reasonable temperature the floor is so cool you don't get that "toasty toe" feel you were going for; or
* The heat responds so slowly that you vacillate between freezing and boiling.

When you get one of those situations, it's usually baked into the tubing that's in the floor, and there's no easy way to fix it. And almost always, what you find is that if someone had jotted a few numbers on the back of an envelope before starting it would have been entirely predicted.

 

[rScotty]

Quicksandfarmer - I am puzzled by your comments as both my house and shop are fully and only heated by hydronic radiant tubing. The shop is slab on grade and the house is basement slab, main level, and smaller upper level. The house is tubing in the slab and the main floor was engineered to hold 1.5" on concrete on top of the subfloor in which the tubing was placed. Another layer of subfloor was put on top of this on sleepers. The small upper level was done with staple-up. Both buildings are SIPs and tightly sealed and very well insulated. Outside Minneapolis. The shop has no issue heating from the floor and it is 2600 sf with 13' ceilings (R48 ceiling).

The house actually runs into problems in very cold subzero weather with not being able to keep up 100% so during long cold snaps I sometimes have to turn on the furnace to help out a bit. The furnace is mainly there for the AC in summer and is used in the fall and a bit in the spring to avoid turning on the floors during times of changing conditions. My issue appears to be the pressure drop in the on-demand heater creating too much back pressure to allow for high enough flow to get enough heat output. from the floors. I think I might have better luck with a tank HW supply, but I am fairly stuck at this point... I tried many things to increase the flow without great success.

Why do you think that increasing the flow will make much difference to the heat in the house?
Have you done some tests? There isn't much of a temperature differential between the concrete next to a heat tube and the fluid inside, so I wouldn't expect the heat to move into or thru the concrete very quickly.

My thinking is that if you are able to ncrease the flow rate through the piping, you will see the return flow will be warmer than before - and the concrete surface temperature will not change much.

But that is just my thinking - not experimental evidence, so it could be wrong. Good thing that being wrong is a key part of being innovative....
rScotty

 

[quicksandfarmer]

Quicksandfarmer - I am puzzled by your comments as both my house and shop are fully and only heated by hydronic radiant tubing. The shop is slab on grade and the house is basement slab, main level, and smaller upper level. The house is tubing in the slab and the main floor was engineered to hold 1.5" on concrete on top of the subfloor in which the tubing was placed. Another layer of subfloor was put on top of this on sleepers. The small upper level was done with staple-up. Both buildings are SIPs and tightly sealed and very well insulated. Outside Minneapolis. The shop has no issue heating from the floor and it is 2600 sf with 13' ceilings (R48 ceiling).

The house actually runs into problems in very cold subzero weather with not being able to keep up 100% so during long cold snaps I sometimes have to turn on the furnace to help out a bit. The furnace is mainly there for the AC in summer and is used in the fall and a bit in the spring to avoid turning on the floors during times of changing conditions. My issue appears to be the pressure drop in the on-demand heater creating too much back pressure to allow for high enough flow to get enough heat output. from the floors. I think I might have better luck with a tank HW supply, but I am fairly stuck at this point... I tried many things to increase the flow without great success.

It sounds like you have a pretty good system.

The amount of heat the floor puts into the house is determined entirely by the temperature difference between the floor and the inside air. So if you find the floor isn't putting out enough heat to keep you comfortable on the coldest days you need to increase the floor temperature.

There's two ways to do that. One is to increase the flow rate of the water. As the water flows through the floor it cools. The faster it flows the less it cools and the warmer the average temperature of the water in the floor. That's what you've already tried, and there's a limit to how effective it can be, the water never gets hotter than its source temperature and at a certain point even ridiculous flow rates don't change anything.

The other way is to increase the water temperature. Have you tried that? A common solution with floor heat is to have what's called "outdoor reset" where there's a sensor outdoors and the water temperature is adjusted according to the outdoor temperature, the colder it is outside the hotter the water is.

 

[rScotty]

There's basically three ways it doesn't work:
* In order to get enough output to heat the place the floor has to be so hot you can't walk on it; or
* The floor puts out so much heat that to keep the room at a reasonable temperature the floor is so cool you don't get that "toasty toe" feel you were going for; or
* The heat responds so slowly that you vacillate between freezing and boiling.

When you get one of those situations, it's usually baked into the tubing that's in the floor, and there's no easy way to fix it. And almost always, what you find is that if someone had jotted a few numbers on the back of an envelope before starting it would have been entirely predicted.

Sounds to me like you are describing a situation where a boiler is running very hot fluid to heat a floor that doesn't have much mass. Most of my comments are directed differently - I prefer heavy hydronic floors/slabs from 3 to 6" thick and running HWH temperatures of up to 120Fmax rather than at boiler temperatures.

But I've actually seen the problems you describe in a couple of systems - one of which i designed myself. That one was built using a commercial system of PEX heat piping inserted into thin extruded aluminum "radiating members" that were mounted between the sleepers under a hardwood floor.
Beautiful installation, expensive idea, poor performance.

Another was an overhead basement ceiling system designed by a homeowner to heat the floor above. It used a solar/propane boiler and high temperatures. In that one, the pipes were fastened between the joists for the floor above in a way that put them in contact with the bottom of the low mass concrete & wood composite floor above. In that installation, the idea was to have the heat pipes accessible from below instead of being buried within the concrete. It ended up requiring hotter fluid than I felt comfortable with, and heated the air below more than the concrete above.

Both systems worked, but could have worked better.
rScotty

 

[quicksandfarmer]

Sounds to me like you are describing a situation where a boiler is running very hot fluid to heat a floor that doesn't have much mass. Most of my comments are directed differently - I prefer heavy hydronic floors/slabs from 3 to 6" thick and running HWH temperatures of up to 120Fmax rather than at boiler temperatures.

The heat output of a floor is determined entirely by the temperature difference between the floor and the inside air. What the floor is made of, how the heat gets into it, etc. doesn't matter. Of course those things ultimately matter, but down the road. If the heating load and floor area of the building are such that you can't meet the heating load with a reasonable floor temperature, that's it. No amount of plumbing is going to change that.

This is what I meant earlier when I said, "if someone had jotted a few numbers on the back of an envelope before starting it would have been entirely predicted."

 

[rScotty]

The heat output of a floor is determined entirely by the temperature difference between the floor and the inside air. What the floor is made of, how the heat gets into it, etc. doesn't matter. Of course those things ultimately matter, but down the road. If the heating load and floor area of the building are such that you can't meet the heating load with a reasonable floor temperature, that's it. No amount of plumbing is going to change that.

This is what I meant earlier when I said, "if someone had jotted a few numbers on the back of an envelope before starting it would have been entirely predicted."

I hear what you are saying. My reply is that it isn't that simple. Some types of calculation may be OK, but the simplest sort of generic total BTU back of envelope calculations can point to the wrong solution by ignoring how a floor will work for the people living on it. Total energy calculations work a lot better for forced air or wood stoves in a room than for heated floors.

An example of things not always is the thermal mass and heat transfer of the floor. Simple calcs say how hot the surface is, but equally important is how it can maintain that temperature. Also, that people will tolerate a greater variability in air temperature than in floor temperature. And I think that plumbing will change both of those things.

I prefer to sum more detailed individual calcuations rather than express them as one single number. That's the only real difference in our methods. Put another way, my feet prefer a different temperature than my hands do.

It's OK by me if you feel differently. And if you get value from doing things that way, then that's OK with me too. Difference is the spice of life.
Besides, I'm old and I'm easy.
rScotty

 

[quicksandfarmer]

It sounds like you have a pretty good system.

The amount of heat the floor puts into the house is determined entirely by the temperature difference between the floor and the inside air. So if you find the floor isn't putting out enough heat to keep you comfortable on the coldest days you need to increase the floor temperature.

There's two ways to do that. One is to increase the flow rate of the water. As the water flows through the floor it cools. The faster it flows the less it cools and the warmer the average temperature of the water in the floor. That's what you've already tried, and there's a limit to how effective it can be, the water never gets hotter than its source temperature and at a certain point even ridiculous flow rates don't change anything.

The other way is to increase the water temperature. Have you tried that? A common solution with floor heat is to have what's called "outdoor reset" where there's a sensor outdoors and the water temperature is adjusted according to the outdoor temperature, the colder it is outside the hotter the water is.

Just to throw around some numbers: imagine you have a house where the heated floor maintains your set temperature when it's 25F outside but not when it's 10F. Additionally, imagine your thermostat is set to 70F, your boiler is producing water at 120F. When it's 25F outside the water coming back from the floor is at 110F and the floor itself is at 85F. What would it have to look like when it's 10F outside?

There are four different heat transfers in this system: boiler to water, water to floor, floor to air, and house to outside. In order for the temperature to hold steady they all have to match. And they're all driven by temperature difference. So let's look at them one by one.

At 25F outside and 70F inside, there's 45F difference between inside and outside. At 10F there's 60F difference, exactly one third more (I picked the numbers to make the math easy). So whatever amount of heat is needed at 25F, a third more is needed at 10F.

With floor at 85F, there's 15F between the floor and the interior. To get a third more heat, that difference needs to be a third higher, 20F. So the floor needs to be at 90F.

With the water leaving the boiler at 120F and returning at 110F, the average water temperature is 115F. With the floor at 85F that's 30F of difference. To get a third more heat that needs to be 40F -- with the floor at 90F. So the average water temperature needs to be 130F.

The amount of heat transmitted by the water is equal to the flow rate times the difference between the out temperature and the in temperature. With the flow constant, to increase the heat transfer by a third the temperature change has to increase by a third, so 13.3F instead of 10F. So if your average water temperature is 130F, and the change is 13.3F, it needs to be leaving the boiler at 136.6F and returning at 123.3F.

In summary, if a boiler setting of 120F is perfect when it is 25F outside, you need a setting of 136.6F when it's 10F outside.