My buff Brahma hen is panting today too! So is my EE roo. It's in the mid-80's here in KY too, and also pretty humid. They have shade and deep grass to lay in, plus two rabbit waterers and the duck bin full of cold water. My smart BO's are taking a dirt bath under a tree in some damp loose dirt...
When it gets really hot I sometimes use the mist setting on the sprayer and aim it in their direction. Some of them love it and others don't. My SF's really seem to like the mist!