83-88*F is perfect temperature. Try using a piece of ceramic tile instead of plywood over the heat mat inside. This will help to dissipate the heat better, and allow a better thermal transferance. If your thermostat is regulating ambient temperature...you're going to need a better one. You want it to regulate the temperature of the mat, not the air. With your UTH(under tank heater, or heat mat) regulated to approximately 85*F, you will be providing a proper thermal gradient. With a "room thermostat" that is regulating ambient temperatures...you are creating a "hot box" for your snake.
In other words...the thermostat you are using is shutting off your heat units at an average ambient temperature of 80*F...or whatever it is set at. This means the hot side is probably too hot, and the heat mat is almost definitely WAY too hot...which explains why your snakes seems to prefer the "cool" side...it is at a more moderate ambient temperature.
So yes...get a thermostat or rheostat that is designed to regulate the heat source with a probe, and a good digital thermometer so you can accurately read the temperatures of both the hot and cold sides of the viv. And do away with the bulb. It is drying out the viv, and creating too much heat.
Oh yea, and...Welcome to the Addiction, and Congrats on the Pickup!! :cheers: