The OP stated the the temps in his (?) house are in the high 80s during the day and mid-70s at night. I think this should be substantial until a UTH with proper thermostat regulation can be put in place. Ideally, IMO, you would probably want to keep ambient temps ~80-82deg in a sick-snake situation, but I would rather err on the side of caution than risk aggravating the burn, especially since there doesn't seem to be a thermostat to regulate any supplemental temps.
I would propose back-heat to be more advisable until that heals up a little though. You mention putting burned hand into a warm oven, I can imagine a burned belly being pretty sensitive to sitting on a warm tank bottom! Ow ow ow ow ow....