Rodents don't do well in places where the temp can rise above 80 deg.
The hay-loft will definitely get a lot warmer than that, no matter where you're living. Even here in the Northwest Territories, I have to be concerned about my budgies getting overheated out in the aviary (fully-enclosed) in the summer. Remember that hot air rises. If the temp in the horse's stall is in the 70's or 80's, you can bet that the temp in the loft above is at least 10 to 20 deg's higher.
You need a leanto on the north or northeast side of a building.