Always go with the temp gun at the surface. With a ground species like a BTS especially, measure at the ground, where he/she will be. The air thermometer is pretty useless.
81-83F is a little high for the cool end at night, but okay during the day. I would want 80-82F tops for cool side temps, if not a little lower, at night. I have day time temps around 80-82F because of a low wattage UVB bulb about 1 1/2 feet away and a higher wattage basking bulb and another UVB bulb on the hot side of Frank's (my northern BTS) tank. He has a 6X2' tank that's 1.5' high. At night, his cool side drops to 78-80F. His hot side is 95-98F during the day (depending on where he is relative to the basking bulb) and 92-95F at night. Ambient during the day is 84-87F and 82-84F at night.
I've had Frank for a while and he's doing great. Not too much out there on these guys, although they are becoming more popular now. I've learned quite a bit along the way. Feel free to check out Frank's thread, post here, or PM me with questions.
Good luck.
Frank's Thread: https://ball-pythons.net/forums/show...ighlight=Frank