In high school in the '70s, Back before I got a helmet, I wore a ivory-colored Kangol 'Tropicap' English driving cap. Then I got a tweed one. It'd even be on my head when riding my motorcycle. I used to get razzed about it constantly. I still wear driving caps, but lined leather ones now since I don't have the 'insulation' on top of the ol' noggin any more.
The top of my head sweats a lot, so in addition to my helmet I usually wear a sweatband when riding in warmer weather to keep it out of my eyes.