I think you will be fine.
The cheese didn't loose form (melt) and It's unlikely the temperature in your cave exceeded the temp at which the cheese was originally made. The culture will still be alive and the damage will be mostly cosmetic.
I have 6 or 7 cheeses in vac bags maturing at room temperature, and they are all looking fine (but, Tas, not Mainland, so my room temp is 18-20 where you were, what 25-30?). I saw a cheese program recently where they were maturing raw milk cheeses at room temperature in the Tropics!
My disaster went the other way and everything froze
The texture was wrecked (although the flavour survived), some of my cheeses I actually saved by melting them and reforming them. Some worked really well, some went a bit grainy (I think I heated them a bit hard) but all remained edible.