I had a leather Aussie type hat that I wore for 2-3 years and love it. Eventually it got kind of stiff and smelly and shrunk from being caught out in the rain. I am actually wearing a helmet now and find it cooler than the Aussie hat. Who'd have thunk!? But that doesn't give good shade.
I guess I saying that some of them can be hotter than wearing a helmet, which actually protects your head.
If I were going for a hat, I would try to find a light color and a breathable material. The palm type sounds interesting.