Is your UTH regulated? If not, pick up a lamp dimmer asap ($10 at Home Depot) and save for a good thermostat. UTHs get to over 100 degrees and can easily burn your snake if it's left unregulated.
I keep my BP's ambient air temps between 75-82, but your hot spot temps are the temps directly on the surface of the hot side (ie the UTH side). This temp should be between 89-92 on the surface, and you will be able to tell the temps of this by get a thermometer with a probe or a temp gun. I use the temp gun myself, and got mine for $30 at Lowes. You can check the cold side temps with the temp gun as well.
Leave the UTH on 24/7, and if you need to boost ambient temps use the light in the daytime too. Unless your house is freezing he should be fine at night as long as he has the correct hot spot temps at night where he can go to.
I still believe that the tank is too large, and if possible I'd move him to a 10-20 gallon. OR...you can move him into a tub setup until he gets large enough for his tank and if you want me to tell you what I do for that set up I can do that too: just ask or PM me.