If you use an indoor/outdoor thermometer with probe the box goes to the cool end to read that temperature, the probe snakes over to the hot spot and lays under the substrate to read the hot spot temp.
If you use aspen or other substrate and don't want to see the wire just tuck the wire under some substrate so it's out of sight.
If the wire runs under a heavy object as strong as they are I'd be worried they would pull the wire and knock over the heavy item possibly hurting themselves.
I've seen them move large heavy pieces of ornamental wood by pulling wires that were running under the wood.
The thermostat probe does not need to go between the UTH and the glass, just use strong tape and tape it against the UTH without taping over the probe(If the room is drafty then do cover the probe).

When you have the thermostat in place and the thermometer in place turn up the t-stat till the thermometer read 90-92 on the hot spot.
Then with your overhead heat move it from hot end towards the cool end till you get the ambient temperatures where they need to be.
78ish cool end and 87ish warm end.

Cover the rest of the lid with saran wrap or foil or both! for added humidity and heat retention.