Ugh, Hera is driving me nuts over the last week. She's been going off property looking for cold concrete to lie on. Inside perimeter of night fence now has hot wire.
No concrete area on your property? Can you get some old carpet? Put it in a shady place and saturate it with water. Check to see if it stays cold and rewet it with COLD water to keep it cool. We used that for the rabbits in the heat of summer. The water evaporation cools it down. If you put in a brick patio in sand (lots of work and needing a brick and concrete retaining wall) soaking the brick will also cool the area with the evaporating. We had one at our old house under the 100-year-old orange trees and I would set the sprinkler on it to saturate the bricks, then it would cool off the area during the day.
Our dogs used to go into the old milk shed at the current CA house, which is about 12' lower than the house elevation and on the east side of the barn, to lay on the concrete floor. DS1 says that Angel is going into the shed in TX which has a concrete floor and laying there in summer heat. Rika and Ozel dig holes under bushes, but Rika also likes the back concrete patio in Yantis.
@Ridgetop Property was bare land when purchased with only the sheep shed which is dirt. Plan is to get some of the extra large concrete pavers and lay them next to water trough drain so I can soak them. I got a 11ft x20ft tarp strung over that area and sheep where taking their afternoon siesta there today.
I spent ALL day moving electric net fence so sheep can graze elm shadier pasture. Unfortunately, it's on north cruddy fence and I'm only reading 2.5kV in fencer there,that is enough. I also have spare water trough on 110ft hose stretched to shady spot in paddock.