“Appears slim” is relatively subjective. Many of the Royal pythons I see online are fat little stuffed sausages. Here’s a picture to give some guidance on that. Also, pictures of your critter would be helpful.
As for you wide fluctuations in ambient temp, it’s likely due to your room temp and only having a UTH. That will do zero for ambient temps at all. If your room is too cool to provide adequate ambient temp then an RHP would be a wise investment to make.
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