Wood floor over concrete?

[Loaderman22]

I deal with this all the time, yes first put down a thick vapor barrier (heavy plastic) on the concrete for a week or two, use good tape to hold plastic. Preferably over a heavy rainstorm. Then peel up and see if any moisture at all. If yes then you're better off with a floating vinyl type floor and wear slippers. If not, then there are many ways to go, but the 2 best options are pressure treated sleepers at 24" o.c. with a good quality low perm Ridgid foam insulation, like the blue Dow board. Then 3/4 Advantek subfloor, (it has moisture resistant glue) then tar paper then an engineered wood floor. You can get good quality engineered maple, and once installed you'll never see the difference. The other option is a multi-density foam underlayment on the concrete, you can search things like yoga or ballet dance floors or multi-density waterproof foam, then install 3/4 Advantek and then your engineered Maple floor.
Heat always goes to cold, so by keeping that moisture barrier and getting insulation under the floor, it will keep the squeaks down and toes stay warmer. If you do decide to do radiant heat you absolutely have to get insulation below the heating source or you will just lose it to the slab and dirt below.

 

[Loaderman22]

R value of 0.55 struck me as a little low and I looked up some reference values

https://www.ahfc.us/iceimages/manuals/building_manual_ap_1.pdf

Hardwood Flooring 0.91 per inch or 0.68 (3/4 inch)
Single Glass 0.91

Perception and memory is funny!

In most parts of NY now, windows have to have a U-factor of .27 or better. The other areas it's .32. a far cry from .91!

 

[dnw64]

And how would you adjust the existing door frames? Most doors don't have ~2.5" to spare.

The OP did not say anything about whether there were doors already framed/installed or not. However, if they were a fairly standard 6'8" door I would cut them down (or is that up?).