How to keep a baby cornsnake warm at night?

So, I recently acquired a young 'Crimson' corn snake. Hes fairly young, still eating pinkies. My concern is how to keep the little fellow warm. I live in the basement, so it gets a bit chilly down here. Currently, my little snake has a 'basking lamp' to keep him warm and a half-log to hide under. However, the issue is that I can't keep the light on at night, it will keep me awake because the tank sits close to my bed. I was told not to use under-the-tank heating mats because it could burn him. I'm just scared that because it gets so cold in the basement that if I leave him without any source of heat he may perish in the night. What should I do? I could possibly move the tank into another room at night, but having the light on him 24 hours a day may mess with his sleeping patterns. Please help! Any advice you have would be most appreciated.