Hey SM,
When I first started growing mushrooms, I always dried them with a screen and fan setup until cracker dry. No problems there. I eventually moved on to using a dehydrator, and while it may be anecdotal, I haven't noticed any loss in potency while using it.
My lowest setting on the dehydrator is 95F. I usually dry my mushrooms between 95-105F and it takes a couple days to dry fully depending on how many mushrooms I'm trying to do at once. You could probably get away with using more heat, but I try to play it safe. In fact, my first cheap dehydrator didn't have any temperature controls, so I have no idea how hot that operated. Still, the mushrooms came out fine.
As I mentioned a few minutes ago in a truffle thread, after dehydrating, I place my cubes into a vacuum sealed bag with a food safe oxygen absorber, then into the freezer. This may be a bit of overkill, but I never understood why that is a bad thing, you know? We spend a couple months cultivating to receive a wonderful gift from mother nature so it only makes sense to protect that gift as much as possible until consumption, IMHO.
I wish there was a way to keep fresh mushrooms fresh though...I love a solid dose of some fresh mush!
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