I’m in NW OR and have shade trees over my turkeys and rabbits that provide shade -most- of the day.
On the hottest days, I freeze water bottles (after draining a bit out of them) and let the bunnies play with them.
(Also on the hottest days) I refresh all water mid day/ early afternoon so it’s cooler from our well.
My ducks have less shade, so I bought rigid insulation and insulated their coop.
They also have a very large, opening window and a fan that is hooked up to a thermostat that I rigged so the fan comes on when it’s hot (reversed the poles, it was easy to do)
I had to add some interior siding to protect the insulation from the birds and the rodents
I just went to the local building materials recycling store and bought the cheapest plywood they had.
Depending on where in S OR you are, you may have better luck looking on CL, FB marketplace, or contacting a local contractor to see if you can find a deal on materials.
Other than adding insulation, shade cloth, and/ or more windows/ fans.... the only other though I have is to look into a misting system.
....which has more downsides and likely more cost than the other thoughts offered on this thread.
Good luck!