Thermostat is driving me crazy!

[KMG]

but it's packing tape so it's really strong. I would be surprised if a snake had the strength to pull up the packing tape even a little bit.

I guarantee your snake is stronger. Its a constrictor and being so it could easily wrap the probe wire and pull the tape up. With heat and age the tape is going to become brittle and lose some power. Even in a weakened state the tape will be able to make a mess of your snakes skin if it gets stuck in it and worse yet if it gets the tape over its face while burrowing around.