A new Ball Python-- But I may have some problems

A new question. It's winter here, and I've yet to find a place to get a thermostat(my
mother refuses to spend money buying one online). I've kept the uth unplugged, but it is starting to worry me. What if my snake gets too cold? Besides the heat lamp, which we have to turn off at night(we don't have a night bulb for him yet), he has no other heat sources. Is there any way I could maybe turn the uth back on? There's a bunch of thick substrate to dull the warmth from it, and I am thinking of ways to constantly moniter(and turn it off) if it gets too warm. I plan on going to the hardware store in search of a thermostat there this weekend, but until then I'm concerned he will get too cold without some form of warmth throughout the night(I live in kentucky, and my mom keeps the house temp WAY too low because she's "hot". So the temperature is usually in the low 60s, combined with how it's down to the 20s outside). He also has a hide(the log hide! I managed to fix it to where no sharp bits are poking out anymore), which has a covered(though hollow so it retains some heat) bottom, and he spends most of his time there or on top of the branch. I wont try to turn back on the uth unless given okay to do so, but I did need to express my concerns.

I feel very silly asking all these questions, and it makes me seem like such a terrible person already 😂
But I want the best for this snake. And even if I have to ask every question in the world, by darn this snake will have the happiest, longest life that a gorgeous snake like it deserves. Even if it starts out a bit rough as we get everything settled and set.

I got to handle him tonight! I reached down in his cage and gently picked him up from his mid body. I even got him to set still in my hand, wrapped around it for a moment. I was a bit nervous, but tried not to show it off to him. I held him for about 10 minutes, taking photos and relaxing. He was very wriggly! But not aggressive. I think he was moreso curious or looking for a meal, with how he kept going his happy merry way and tasting the air. The other morning I saw him yawn and I seriously teared up. Maybe I'm a bit too obsessed though, everything that's been coming out of my mouth is "Twitch did this, or twitch laid in his log again and peeked him little face out. I read online this. Blah blah blah" I've about talked my sisters and mother to deaf. I want to be a herpetologist and exotic pet vet one day, as here in Kentucky there are none. Onto my question at that note. When I held him, I was looking for signs that his belly was burned during when I did have the uth on. His belly is different shades of yellows and light browns, with some white spots on the tips of the scales. Is this just a part of the spider morph, or did the short time I have the uth on burn my snake? They weren't neccesarily pink or anything.