I would not worry about the lubrication. I'm confident that it was specified to survive 100 degree temps. Mine has. The temp of your gear will rise and fall slowly with the temp of your house. I'd worry more about ensuring that the gear has air to breath to avoid condensation rather than any extreme measures like refrigeration. Moderation in all things is a good thing, except perhaps love... in which case, the more the better.

The foam degradation issue was most likely old chemically-unstable foam, not heat.