Further dorkification evidence for you - I wear a cycling cap backwards under my helmet. It makes a good sweat absorber in the summer (and a good cooler if rinsed in cold water) and makes a good head warmer in the winter (if I need more warmth, I add ear covers or a rain cover/helmet condom). I will occasionally - meaning rarely - wear the cap forward so as to use the bill to block the sun. I'm not particular about whose cap I use, as long as it can stay put on my Chombi-like head when the helmet is on. I'm currently using a Riv Atlantis hat despite the goes-with-absolutely-nothing color because it fits, is reasonably substantial, has a good sweat band and holds up to washing better than most.