A headband will do the job perfectly, preferably a cycling type as the normal type are normally made of towelling type fabric. The cycling ones are a lot thinner. I bought two from Prendass, Team Highway ones, and you do not even notice you are wearing one. looking on the site though now, they do not seem to have them in any make.
As for the wearing of buffs and caps coming into the equation I do not know, its totally ilogical on a hot day, probably just a fashionable trend but all they do is retain heat underneath which makes you even hotter, one minute its acceptable to wear a hat to keep your head warm and then another day, to wear one to keep your head cool. Let your hair serve one of its natural purposes and let it wick the sweat away as the air flows through your helmet. I cycle with a few colleagues who wear caps and buffs, but it soon becomes evident that they are overheating by the red faces and eventually have to remove them or suffer along with sweat running down their faces. Keep them for the cooler days when they serve a purpose of keeping your "napper" warm.