cold crashing

I'm wanting to cold crash my esb but the in-laws haven't gave me there fridge like they said there going to and my beer has hit it's fg so what I was wondering is that's since it has gotten cold here if I could but it out in the shop it won't be as cold as I would like it to be but the temp won't be steady. So I was wondering if the up and down tempos would hurt the beer n try to find a diff why of doing it. N one more question if I do cold crash it when I go to bottle it and let it carbonate it will warm up now why that give it off flavors

You can cold crash your beer anywhere it's cold. Colder temperatures help to drop sediment out of solution faster.

You don't have to worry about off flavors when the beer is warmed up for bottle conditioning. Warm temperatures create off flavors during fermentation, particularly during the initial part of fermentation.