Shade would help.
A cheap fan if you have electricity.
Can you plant anything in /outside the run?
I dug holes in the run on some really hot days so they would dust bathe in the new holes. At night I poured water in them to moisten the soil. Water evaporating pulls off heat. Some chickens might freak out if your digging around in the run but mine run over if they see I have the shovel. Heck I have to shoo them away just so I can dig. Mine know shovel+ digging= yummy worms/bugs. They stand right on top of the dirt I am digging out.
I know someone that tried the ducks and chickens together with a small pool set in the ground. Ducks love it but chickens will drown. They found out the hard way. It wasn't very deep but the sides were sloped. The chickens would try to walk out of it and slip which dunked their heads. He only lost one but another was in it and before we got it out I saw how they drowned in a 6-8" deep pool. The pool situation was fixed.