Im not trying to bring you down. Im trying to understand the purpose of the build. I just don't understand what we are fixing here. Im also trying to make sure you are doing this having thought about all possible issues. Im seriously just trying to help.
Any CHE, bulb, other heat source should be controlled. Be that with a tstat, dimmer, or distance. They should ALL be monitored and controlled. No matter if they are inside or outside.
Now what I don't understand is how the setup you created is going to provide a proper hotspot once it is set up over a cage. At only 180 the fixture is going to need to be really close to the surface it is trying to heat. If a CHE is properly placed outside of a cage and needs to run with a center temp of 500+ to create the correct hotspot on the surface of the hotspot that is just what it needs to do. It is no danger to anything when done correctly. I can assure you that regulating my CHE to a safe to touch temp will never give me what I need to heat my ETB.