I would definantly give that a try. I would just be worried that the texture might change once transfered to the fridge. Hopefully it will keep the same consistancy, color, etc.
My cream color base would "sweat" when it got too hot. But I actually liked it cause it was easier to put on. When it was winter, it was very stiff and I held it close to hot water to warm it up. Maybe put it in the shade somewhere?
I would say take them off of their sides and lay them down flat.. in a closet or some place cool but room temp. and let them settle them selfs, there are a few cases out there that are good for being good in the heat as well.