I like to turn them off at night. It's pretty warm in here, and I would rather simulate a real outside environment more by lowering heat and light at night. Plus, that constant heat speeds metabolism (ultimately a shorter life).
Plus, I think you'd have to think about the material the lamp is touching. If it's some sort of fabric or synthetic fiber, you could start a fire or melt it (and glue). If it's a metal screen, the metal will get extra hot.
Sometimes I like to go to the craft store or random places and see what I can turn into a mantis house. Today I found some storage containers that look like paint cans and some circular cross-stitching dealies.
I trimmed the circles to fit and glued the tag to the side of the can as a hinge...