Shade is a must. You'll see a few options in photos in Hacks-n-Pups including my tonneau cover with a zippered hatch for Barley. It works, but does cut down on airflow so in the future I might go the ragtop option.
At the MOA rally in Missouri we rode in temps ranging from 94 to 108. Hydration was key! I had trouble getting Barley to drink piss warm water, so every morning I'd fill a small Igloo cooler with a bag of ice. By the time it got hot there was enough ice water in there for both of us to have some at stops, plus enough for me to soak his belly and my shirt to get some evaporative cooling going.
In case of breakdown at the side of the road I carried a small Noah's tarp with poles so I could at least get him out of the sun. Also, at night it didn't drop below 100 till 9pm, so I carried a battery powered tent fan just in case.
Hope this helps.
I got a sidecar to travel with my dog. He never complains, is delighted to be with me, approves of my dietary choices, is a social butterfly who helps me meet folks, appreciates a good beer, snuggles better than my wife, and hangs on my every word as if it's the most profound thing he's ever heard. TravelsWithBarley.com