Hi. Telling whether or not your hermit crab is really dead or not is pretty tricky sometimes.

First of all, I need to ask you a few questions.
Was he above sand, or trying to bury when you noticed that he could possibly be dead? Generally a crab that is deceased will bein to fall out of their shell, or smell really badly. I would give it a little bit of time, since you don't want to throw him away if he's really alive.

You don't need to have a lamp above the cage, unless your crab doesn't get any other type of light- or if the cage doesn't stay warm enough.

Hope this helps
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PHStorme