What kind of rat snake is it? Corn snakes are a type of rat snake. And not providing heat seems like a bad idea to me. Reptiles need a hot side and cool side to thermoregulate. You are forcing your snake to stay at the same temp. If i were you i would get a thermostat and a temp gun and adjust the temps to your snakes liking.

And snakes have been found basking at much higher temps then what most of us keep them at in captivity. 110F is really not all that hot. It cant burn a snake or even a person. My snake also has the option to bask at much lower temps if he chooses.

Normal basking temp for a corn is around 85F. My snake does use the high basking spot daily as well as the lower temps. I keep my humidity around 60%.