Why should dried mushrooms be soaked in warm water?
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.