We just usually tried to keep King in during the day or stuck to shady areas. We were lucky that for most of his time with us that our neighbors had tall trees.

On car rides I put a while cloth over him.

I'd say go to a fabric store and get a few yards of a thin white cloth similar to what bandannas are made of . Something light and breezy. Make a light weight slip cover sort of thing for him. Make sure to make it a bit loose. Have it so it goes up the neck a bit, attaches there, and a strap for under the belly to hold it in place. It really does help out a LOT.