I want to say this is impossible. For the fact that a non regulated UTH can get above 130 degrees. I don't care how thick the glass is, it is hot enough.
I am guessing your method of measuring temps is wrong. Temps need to be measures at the ground level under substrate. BP's will burrow and if you measure temps other than the very bottom the snake could burn him/herself.
On a side note with such a low night temp you are going to have to insulate the tankglass with corkboard. I would also suggest wrapping the tank in flexwatt (3 sides) and set the tape at 80 degrees then use a UTH to heat the hot side to the 92. That should help keep temps normal 24/7.