If you can freeze a big block of ice (re: gallon jug) and put just in front of fan, that will help too. But I agree, an awning will help keep the area/side of barn from getting as hot as it does.Option E frozen h2o in nest box is a great idea!!
My big issue is in the evening when everyone roosts for the night, that side of the barn is just hot hot hot.... I now have the box fan in there - was looking for a portable AC unit but they are so darn expensive.
I think if I do what @BY Bob did with an awning it will cut down on sunlight streaming in and heating things up - and keep the box fan in there.
I think heat is far worse that cold in many cases.
(FYI: I keep a few gallon jugs in freezer so can swap them out if needed. Just remember to not fill completely full & 'squish' the sides in before screwing the cap on, so it doesn't burst the jug as it freezes.)