Can you ever get a thermostat? I think I would put a piece of slate or thick ceramic tile over the UTH, with the rheostat at the lowest setting, and check the temp after about 12 hours. You need to have a tile that is flat on the bottom, not grooved. Or turn it over to the top is facing down, so there is no possibility the baby would get under it. Some people do keep hatchlings with a warm area of up to 90F, as long as they have plenty of room to get away, but that would make me uncomfortable. If you can get to 86, 87, I'd feel a lot better. 84-85 would be good, given your warm room temps.
When you have an adult snake, 80F without heat on for the summer is fine.