Well, this isn't what you are talking about, but it helped me. I had a lot of trouble with wind making my eyes water (I wear glasses). I ended up buying a cap - one specifically for bicycling which basically means it is made of a wicking material and the brim isn't so stiff (a normal baseball cap brim could do a nasty job on your scalp in an accident).

Actually, I have two of these caps with the main difference being the size of the brim. It does help a lot with my problem. You do have to be aware that if your head is down much, the brim also cuts off vision - basically the part above the top of the glasses. Since the brim curves down on each side like any ballcap style, it has more effect in that area. You just need to be aware of this and use caution.

It also helps a lot with getting hair messed up. You don't get corn-rows from hair being sucked up into vents and your hair stays drier too.

I haven't had any issues with it being hotter on a ride, though I don't know how it would be in really hot areas.

Both mine are made by "Headsweats" and I usually use the one with the smaller brim (the "Salsa").

Bob