It's probably just fine to relax.
While technically heat, humidity and temperature cycling aren't good for the cards it's more of a concern if you have poor storage materials as the heat will affect them more than the cards. Most modern storage materials are mostly ok in heat.
While I don't live as far south, we see 90 pretty often, and the occasional 100+ here in Mass. My house is from the 1880's and has no AC at all besides a couple window units and neither is in the room the cards are in. The places before that were pretty small, and had long stretches without AC. Other than the last few things I had in old vinyl pages, nothing has been affected at all. Even those weren't bad, the pages stuck to each other but didn't damage the cards.
Some collector a long time from now may curse me for not having a proper climate controlled room with backup power, but for most of us that's just not realistic.
Steve B
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