Can I use duct tape to tape down a thermostat probe for a snake tank?

Personally, I don't use anything sticky inside my enclosures. Any kind of tapes or glues can get stuck on the snake and pull off scales or cause other damage. I would use a suction cup. You can find some in hardware stores that are designed for holding cords in place, they usually have a slit in the back that allows you to run the cord through the knob on the back of the suction cup. Perfect for securing cables inside enclosures, and even for holding vines and things like that in place.