My coop is 16'x10' and even though it has 5 windows, a door window and a ridge vent, and 2 gable vents, it was always sweltering in there in the summers. I got a box fan and put it on the end window, with a 1x2 piece of wood to keep it from falling backwards, and keep it on high almost all summer. It did wonders. Even though the temp is still high, it just feels so much better. This fan blows outward.
When its really unbearably hot, I set another fan in the front storage room, right behind a screen door and turn it on. The chickens love to lay right in front of it and cool off.
I thoroughly clean the fan every fall or spring, since it gets pretty darned dirty. A leaf blower works great for that.