I'm no automotive expert, but electronics is my field of work. I'm guessing that the $37 is going to be the way to go. First is the resistor your talking about "encased" in a square plastic housing or a round tin housing? Do you know which wires are comming from the switch and going to the heater motor, and is there only one wire for the motor or a few. The problem with only putting in a single resistor, is that if a single wire is used to feed the motor you may backfeed your new resistor when you apply voltage to the other settings. This may or may not present a problem, depending on the switch. To eliminate this backfeed a proper sized diode is needed and put in the proper way. You will also need to know the resistance (Ohms) of the resistor and then purchase one that will handle the load (watts) that is needed. Here is a rundown of Ohms law which will help you.
V=voltage
I= curent (Amps)
R= resistance (Ohms)
V
------
I * R
V= I*R
R= V/I
I= V/R
Another important law that you'll need is the power law. And you thought this was going to be easy
P= power (watts)
I= current (amps)
E= voltage (volts) (some folks will forgo the E and put in V, both E and V = voltage).
P
------
I * E
P=I*E
I=P/E
V=P/I
Once you find the resistance of the resistor you'll need to convert that to current (amps) I=V/R. Example 12volts/6ohms=2amps
Now that you have both current and voltage you can get wattage, so you can get the proper sized power resistor.
E*I=P Example 12volts*2amps= 24 watts
so in our example you would need a 6 ohm 24 watt resistor.
Call the autoparts store and see if they can give you the size of the resistor, otherwise use the formulas above.
FYI the reason the light dimmer didn't work is, it is a triac that is designed for AC only operations. A diac would work though.
Hope I didn't confuse you too much and I hope your laughing and I wish you well on the repair. Even though I deal with these things daily I'd spend the $37 and get exactly what you need.