Chins don't pant, as far as I know. Signs of overheating include but are not limited to:
Red/hot ears and/or paws
Bulging veins on ears
Lethargy
Sprawling/laying down
Do you know what the humidity is also? 76 seems too hot, but no one can really say what the limit is for each chinchilla. Most likely your chin is warm, especially if it is humid. I would get an AC tomorrow if you know you're AC (central air? or other window unit in different room?) won't lessen the temp any more than 76. Until then, frozen water bottles in the cage (I wouldn't leave them overnight because the precipitation would leak in the cage unless you can wrap them in fleece), you can put the slab in the freezer for a bit (usually they'll stand on it just to investigate what it is and mine always licks it, heh) and don't do playtime as he may overheat himself.
My chin was at my parents house this weekend and it was 75F, 45% humidity. I was worried and I kept her close to the AC vent and had ice in her cage etc. At night, when it cooled down I took her out once to play. She did ok, but I had to watch her since I knew she could easily overheat. Every chin is different, so some other chin in Chloe's situation could have been worse off. It would give you peace of mind to not have to worry when you leave the house is Cosmo is going to get too hot or not.