The UTH or heat tape would go on the outside floor of the cage. Use foil tape that you get at any hardware store. https://www.homedepot.com/p/Nashua-T...7792/100030120
Tape 3 sides of it down, then slide the t-stat probe between the heat tape and the floor of the cage on the outside. Then tape down the 4th side of the heat tape.
Then set the temp on the t-stat to 88F. Wait an 30 mins to an hour and then check the temp all over the heat tape with a temp gun from the inside of the floor of the cage with no substrate on it. It will vary as heat tape isnt 100% uniform. You want it to average around 86-88F. A spot of 90F or a spot of 84F isnt going to hurt, you just want it mostly around 86-88F.
Once you get that set, you are done there. Cover the floor with no more than 1/2 inch of substrate.
Then for the CHE, if you are using a t-stat for that too, put the CHE on the same side as the heat tape. Then adjust the height to where it is just above the screen top. Hang the t-stat probe inside the cage on the cool side just above the height of the snake so it cant sit on it, poop on it or otherwise affect it. Then set it to 77F. Once it's 77F on the cool side, temp gun the top of the substrate on the hot side and see what it reads. Also, the CHE should not be on 100% for long, if it is, you have too small of a CHE and it is working too hard.
And for the cage itself, cover 3/4 of it with tinfoil. Cover the sides with rigid foam insulation like this stuff https://www.homedepot.com/p/R-Tech-1...0817/202532855. You basically want to insulate the glass since your room gets so cold so the CHE isnt working 24/7 overtime.
Alternatively, you can also place the CHE in the middle of the cage and do the above as well.