When wood touches a CHE, the wood combusts, first into a black blemish (Charcoal), and further to possible ignition. I forget the ignition temperature of dry wood.
As far as CHE fixtures go, IMO they are not safe. If the fixture has a blockaid of widely spaced steel mesh, your ig can jump up and grab it, then lift his body so he can get a good hold with his back feet. he is likely to hold that position until his belly is severely burned like a potato chip. When I was a beginner, one of my igs did that, and received a belly burn from his neck to his vent. It took vet care, but he survived. The vet figured the hab temps were too low, causing the ig to seek higher temperatures. The trouble is, iguanas can't feel heat very well on their bellies. So I wracked my brain to figure out how to safely mount a CHE within the cage that he couldn't climb onto. This is what I discovered. If I hang a CHE in a simple ceramic lamp holder, my igs could jump up beside it but could not get a foot-hold. So from then on,, all my CHE's hung by their wires from habitat ceilings, and over the next 15 years had no other CHE burns. I used that method with A-type household lamps (bulbs) too.