You're taking a gamble keeping him without a thermostat. So far you've been lucky and getting all the high luck dice rolls but that doesn't mean your snake is safe. He will get burned, despite you being convinced you've tested and closely monitored, it's just a matter of when and worse, when you're not around. Show your parents what a burned snake looks like, and it's not impossible for a unregulated uth to melt through.
As for not eating, in addition to the questions already asked, have your parents been handling him? That could be another reason why he's refusing.