Worried About High Tempature in Bedroom at Night

My LO is almost 8 months old and the shitty apartment my husband and I live in has no central AC. We live in Florida and the heat has been killer. We can't get our apartment colder than 82°F at night, and we're worried about SIDs due to high heat. We're getting a portable water cooling fan, but we're waiting for it to come in. We've tried everything to get our place to cool down, and our apartments aren't doing anything to help with the wall unit that's giving out due to the heat. Are there solutions we should be considering and how do we keep baby cool aside from leaving him in just his diaper alone in his crib?