That's good.
Ppl here are all gonna say Thermostat. The 500R doesn't but the Ranco's, Helix and what nots have a fail safe on them to not over heat devices their heating. As long as you check the temps youll be fine. Thermostats just keeps my mind at ease knowing if I'm gone awhile it won't get to cold or hot. I had my Spider in quarantine with a dimmer on the UTH so you should really be fine. All that really matters is that it's controlled seeing they reach temps around 132 my accurite read one time when testing the UTH.
As long as you ball eats, poops and pees and you meet the normal husbandry temps and humidity requirements then you all good.
BTW side note:
Im guessing you own a 2004 5.7L GTO?