I have read that 100 degrees F is their line -- although reading on here makes it apparent there are variables, particularly shade and breeze, also hydration, etc. It does reach 100 or slightly over here, and we have not lost a chicken to heat in the few years we've had this flock. Mine were moved to a defunct garden a couple of weeks ago, which is still grown up with grass, weeds, etc., so the soil stays somewhat cool and moist from the vegetation. I still see them mouth breathing and holding their wings away from their bodies at times, so I know they get warmer than they'd like to be. On occasion I have dunked a chicken into a bucket of air temp water and let it air dry -- which stops the panting and wing stretching. I've never brought one in the house to get it cool. I do other things with water if needed -- cool the coop or ground, water the weeds so they drip and stay wet a while, etc.
I do feel part of the reason we haven't lost one is, they are acclimated. This is the down side of using A/C -- or heat in the winter.