Another vote for the French-foreign legion cap or pirate's cap back-of-the-neck cover. On my last tour, I covered the back of my neck and ears with a bandana made of synthetic material, and it made a tremendous difference.
Also, I wore a long sleeve jersey for the first time. Contrary to what I expected, I actually felt cooler in it.
I also make an effort to stay out of the sun during the hottest hours of the day. I have taken naps under shady trees, read books in cafes, window shopped in nice towns, etc. One of these days I would like to go to a matinee during a tour!