I guess you'd have to experiment with different wattages to see if it:
1. Provides enough heat.
2. Heats up fast enough to make the AC react when necessary.
3. Cools down fast enough so you don't overshoot.
Any electronics supply would have resistors. If you use the ranco to switch the hot side of a 120v supply, the resistor would attach to that switched hot and the unswitched neutral. You'd want to be really careful that you don't leave any part of the wire or resistor leads exposed. In that regard perhaps a 12vdc supply would be safer but the resistor values would change.
12v / 100 ohm resistor = .120 amps and 1.55 watts. You'd need a wallwart that was capable of at least 200ma. I'm not 100% sure if 1.5 watts will be enough heat fast enough. It won't hurt to try though. If you need more heat, a 50 ohm, 10watt resistor
50 ohm 10W 5% Wirewound Resistor (2-Pack) - RadioShack.com would give you 2.8 watts of heat and you'd need a 12v, 300ma (minimum) wallwart for that.
It also wouldn't hurt to put a 500ma fuse inline with one of the wires from the power supply in case of a short circuit situation.
If the shutdown lags too long from residual heat on the resistor, you could try not insulating the bundle at all and just wrapping it with tape so that the coldroom air affect the bulb faster when the heat is off.