How to work with Dried Mushrooms

Mushrooms should be stored in the refrigerator in a breathable container. A paper bag works great. Mushrooms stored in this manner should last at least 4-5 days.

For the record, the top of the fridge is one of the worst places to store foods. Depending on the model it can actually be a few degrees higher than ambient temperature, thus accelerating spoilage.

Rehydrating dried fruits and vegetables in warm water is fast - mushrooms might take 15-20 minutes, though some varieties take longer, and it of course depends on how hot your water is. It would take a lot longer with cold water. You can still do it, and possibly more of the flavor will remain in the mushrooms (since you're not effectively cooking them slightly), but it'll take hours - not the kind of thing you can do without advance planning.