I live in the Northeast but even here summers get brutally hot. I have a walk-in coop (5x7) with lots of open areas - wrap-around 6"-tall vents at the top of all the walls, plus two large windows and the human door is replaced by a screen door in the summer. I have two fans in there (cheap clip-ons from
Amazon) - one is in a window, to draw cooler air from the outside and blow it at the roosts, and the other is up at vent level to get air moving through the vents.
Despite all that, it gets ridiculously hot in there in the summer (I have a remote thermometer inside). The biggest problem is inside the coop, not outside. The coop is a shed-like wooden structure with a shingled roof. It's under a large tree. And with all the open vent areas. It still gets up to above 100 degrees inside, often 110, and retains heat well into the night. It never gets that hot outside, barely breaks 90 most days, just high 80s and very humid. My run is very shady. So the chickens are okay during the day, but pant at night. So, in my case at least, the problem is inside the coop, but there isn't much else I can do. They have food and water outside in the summer, so they have fewer reasons to go in during the day, and at night, it starts to cool down in there a bit after midnight, it just takes it a very long time to even out the temperature with the outside.
So I'd say open up as much as possible, replace the human door with a screen, open lots of windows, replace a whole wall with HC if you can. And yes, the fans help, too. I had mine set on a timer, to only blow when the chickens are inside to sleep at night. Didn't have any problems with clogging or dust or burning out.