Originally Posted by
catonec
I wear those stupid little cycling caps under my helmet, they possess almost no thermal properties but absorb the sweat like mad. headsweats make the best one imo.

What he said. They are a lot thinner than baseball caps around the brim and will be more comfortable under a helmet. But again, it may look silly to you, or it may be small enough to loose. Buy a day-glo orange one.