Yup I would of recommended a CHE (ceramic heat emitter) instead of the Heat Lamp. They dont dry things out as bad and cost about the same but they still kill humidity.. as far as the Heat Mat (Uth) they are only for the Hot spot and thats why it didnt warm the tank.
Let me give you advice for the situation your in... this is based on a limited budget and the fact your using a Glass tank. Ditch the Heat Lamp, get another UTH and heat the entire floor of the enclosure. This will accomplish a couple things. One you wont dry your tank out and the other UTH will warm the water eevaporating it and creating humidity, and 2 wherever the snake is it will be within safe temps.
You would set the Hotside mat to 90 and the Cool side mat to 80.
Now on another note, your tanks small. I would NOT buy another UTH for that small tank myself, I would find a 40 gallon Breeder. You would need the Big Heat mats for a 40gallon Breeder tank. Then the 2 Big heat mats would basically touch eachother heating the entire floor. If you buy a smaller mat now for that little tank you’re basically going to throw that money away when you upgrade and that tank is too small. However I have bought and sold things I was done with on FB marketplace for years now... so you do whats best for you.
WE all kept SNAKES in this fashion 30 years ago with only heating the floors (heat rocks and heat mats) so this works just fine and will keep your snakes healthy.
It’s not the advanced way of course but I’m giving you a healthy & Safe way for your situation.
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