You can hot glue the probe in place. Just glue the wire behind the probe not the probe itself.

I don't have those cages but do have some RHPs in some. They didn't work for me and I chose to heat the room instead of mess with them. I was trying to heat 4x2x15" cages and the cool side would not get warm enough.

I do use one for my GTP and it works great to provide his hotspot.