The "final solution" is to lose enough weight that your thighs don't touch, and therefore chafing is never an issue.
I used to (and am starting to again recently) run 5 miles and bike 20 miles a day; no matter how hot it is, if you are "in shape" enough the chafing is never a problem. Furthermore, if you exercise that much, you will almost never sweat (brow or otherwise), so you can just keep a steady pace and not be wet.