Wow that's hot! I'm not used to temperatures like that on more than 1 or 2 days a year. I'm not familiar with temperatures that vary as much as yours but I would be looking for somewhere to store my beer, either a friend's basement or a dedicated beer fridge. Having bottles go from 70* up to 90* and anywhere in between at night couldn't be good for them.
Having said that, I'm not speaking from experience here but during the summer I don't brew in my apartment (gets as hot as 80* on some days), nor do I store any beer here other than whatever is in my fridge. Thank god I have a mini fridge that I can fit 60-ish bottles in. I do all my brewing in my girlfriend's basement where it stays 70-72* all year long.