Correct me if I am wrong but do you only have one thermostat? On the UTH?
im not sure if you were asking how to control the lamp or if you should.
Either way the answer is YES. If you don’t have a thermostat for the Heat lamp you should unplug it and go get one ASAP. Heat lamps get insanely hot. And yes your snake could move away from it but Oran not ideal and could really close off that new big tank you just got or worse yet harm burn or cause a plethora of other issues.