It depends on if that screen is accessible or not. I used to use my dome light straight on top of the mesh, basking branches 8 inches down and the screen top wasn't really accessible.
well my bulb is 5 inches up inside the dome so do you think this would cause a problem? i use a 60watt and my 10 week old panther likes to get close to it.although the mesh is just warm and not burning hot,surly you would be able to tell if it was burnable?