Without personally monitoring and being aware of the temps in your room at all times, it would not be wise for anyone here to tell you whether or not you should turn it off.
With or without a UTH, you should maintain a heat gradient in the tank...92-94 on the warm side, 82-84 on the cooler side. That kind of gradient won't happen if you rely solely on the ambient temps of your bedroom.
So long as the UTH is hooked up to a reliable thermostat, it will be safe and not "cook" your snake, even if the room warms up.