All UTH NEED a T-stat or you are just asking for a burned snake. If you are in a pinch, call your local grow stores or nurseries and ask for a hydrofarm digital thermostat. They are around $35 and will work but they have a temp swing of around +-4F. In the end though, you will probably want a Herpstat. I personally use both and they both do a decent job. The Herpstat gives much tighter swing on temps with a variance of only like 0.9. Bottom line though is get a T-stat for sure and when you take the temps preferably with a temp gun, take the temps from the bottom of the tub, the spot closest to the UTH.
Basically when you set it up, you put the T-stat probe between the UTH and the tub on the outside of the tub. Generally putting probes inside the cage on the floor is just asking for a destroyed probe by either water bowl spills or the snake pissing all over it. The Hydrofarm probe is part of the unit so if it gets destroyed, you got to buy a whole new unit. Herpstat ones are replaceable but again, you would need to order one which will take 3-4 days to come in. Once you get it set up, then set the temp to around 90F. let it warm up and then use your temp gun to verify that the bottom of tub is 90F. Adjust as needed to achieve that 90F bottom.