I don't like wearing hats to run it usually makes me too hot but, in the hot spell I've been wearing a Rohan skip cap, it's very light and surprisingly cool, with a handkerchief type bit at the back to protect your neck -Foreign Legion Style- , but so as not to look a complete idiot, I soak it in cold water (wring it out) and put it inside the hat, keeps the head really cool. I think Nike do one as well
