If it gets really hot.... I would be tempted to completely remove the shed wall that is against the run...
So make the shed with 3 walls... 4th wall wire, or if you are confident in the security of your run...just open to the run.
I would put a window on the opposite side of the newly open wall... so that YES wind can blow right through and directly over the perches.
My sister in Texas has her coop set up so the entire top half of the coop walls are wire.... so yes the wind blows over the perches. She very rarely has snow, so it does get cold, but heat is her big issue. The open coops fix that.
My sister though has deep eves, that shed does not.... so the window that I suggest putting across from the new open side.... would have to be closed in storms or set up with an awning or some kind of rain protection since wet birds are bad... need to keep the rain out.