Tripper,
I put in two lights inside each door--for general lighting and something to easily turn on when 'coming home' i.e. these are NOT our reading lights, which are LED's.
The two lights came from an auto supply store--there retro dome lights with incandescent bulbs. They came with an insulation to mount underneath them--a 'felt like' material, which I think you can get at any electrical supply store.
Also, I did a test...I put the light on a piece of luan....turned it on and ran it for over an hour. Then I felt the wood behind it and it was barely warm (I did the test WITHOUT the insulation) Now, the reason the wood did not get hot was that the baseplate of the light has 4 'nubs' which raised it off the surface of the wood...but, screwed down, I think the insulation would be a must. If you can't get LED'[s for your fixture, get the insulating material...
Jim