So, I started a post about how I figured it's just a surface area to volume thing, men have more volume and less (relative) surface area to cool themselves with. So, I was curious and decided to check into it, as it turns out
men just sweat more. I wish I had access to the full article to see if they proposed why women would have higher efficiency evaporative cooling.
As far as men and women cooling themselves via different methods, ie radiation for women, convection/sweat for men, I'm not really prepared to believe that right now. Where did you hear that? Could you post a link?