Jay8
Any heat producing device better not get hot enough with covers installed to ignite even gasoline soaked cheesecloth. There is no code prohibition against the steam generator being located in a closet. I appreciate your thinking but it is not prohibited to my knowledge.
I would assume you have seen hot water tanks buried under old newspapers and other stored items. Your steam generator is touch safe except perhaps the outlet pipe which should get insulated like any steam pipe would.
