this summer we had some hot days, the Delightful Dozen panted like you described.
We froze some large plastic waterbottles and placed them around in the run - that was not so popular with the girls.
We ran water and made a "mud hole" that was a favorite! They liked to lay in that area even when the water had soaked in.
But the thing that worked best was to give them free range in the yard so they could find a comfortable spot. They did fine after that, now they free range in our large fenced yard all day long, they love it and I love the 8 eggs a day we get on a regular basis.
Good luck with your flock!