There is going to be a big difference in temps between the bottom level and the top. You'll likely need either a thermostat that can handle 4 different levels, or 4 different thermostats.

Personally, I would have gone with a radiant heat panel over a light bulb. Wont suck out the humidity, and your snake isn't likely to burn himself on it.

I would test your cage in the final room for a week before putting in any snakes. It should be with a thermometer that can record high and low temps like the standard accurite thermometers. Also, checking throughout the day with a temp gun just to satisfy.

I'm telling you, it's going to get very hot in there. Do you have a lamp next to your bed or somewhere close by? Those lamp bulbs get incredibly hot, you really SHOULD take people's advise and install a fan system in the back.

I figure you will anyways once you record the temps your going to get in there. I imagine the top three levels will be very warm on the bottom of each cage because of the rising heat, and the lowest level will be quite cool.