Basking light shouldn’t theoretically need to be on a thermostat if you secure at the right height for the desired basking temp directly underneath of 95-100(this is where a temp gun is useful) but any ceramics will need running on a thermostat.
The basking light will feel hot to the touch, definitely don’t touch the bulb directly, I am also noticing your dome is being held by a clamp, the clamps have been known to fail unfortunately which makes them a hazard, I’d get yourself a stand, or better yet make one out of some timber, screw to the side of the enclosure, then hang it using chain, you can get them on rolls and chain clips🙂something like the photos👍
Also if you aren’t using any ambient lighting, make sure the room is nice and well lit during the day, though an led over the enclosure would be ideal😊
