I would not recommend placing a heat mat inside an enclosure regardless of how it's regulated.
I suggest you remove the heat mat, and replace the spot lamp with a Ceramic Heat Emitter, you'll want to use the lowest wattage you can get away with so if your thermostat fails it won't kill your snake.
Also, if you don't have a thermostat, then I'd recommend ordering the InkBird WiFi off amazon, it's $50 so not the cheapest, but the best value you'll find.