If your refrigerator isn't below about 40 degrees, then your food isn't safe! You definitely want to store food at 40 degrees or cooler, so that would be a big concern to me if the fridge is too warm. Unless it's a beer fridge, of course, and you like your beer closer to 50 degrees.
Either way, the fridge should be at least 10-20 degrees cooler than room temperature which would work fine for a cold crash.
Do not freeze the mead!
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