Use a small cold/wet towel around the back of the neck while walking or riding.
I'll place it on the top of my head for a moment, then wrap it around my neck.
I'll also make it a point to stand off to the side of the green until it's my turn to play.
Green's are like saunas and humid.
I also like playing with three or less players when temps get over 100.
That way you spend less time on the tees & greens.