I have some rhp in my large pvc cages(48x24x15). My home stays at 68 and even cooler in the winter and trying to use the rhp alone it just didn't work for me. I had to start using a oil heater to heat the room.
Mine are not thick though so I bet you will have better results. Be carful as the taller your cage is the stronger rhp will need to be and the more heat it will have to pump out. You really want to stay under 18 inches. My 15 inch cages hold a brb and a big blood and I like that height. Any shorter and it would be hard for me to clean. I think 15 is a good median.
To mount my tstat probe I use a cable strap and super glue to mount it to the rim of the rhp. It appears the probe touches the rhp in the pic but it doesn't.
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