Grump
We have similar problems here in the tropics. Also we don't have the choice of going helmetless in this country.
When the heats up I use a bandanna that has some special beads in it that make it stay cool for hours, either just wet it or put it in the fridge wet for an hour or so and it'll keep your noggin' nice and cool between stops. I actually got it from an industrial safety place, they promote using them under the hard hats as thats where most heat is emitted, even worse if you got a nude nut like me.
The other thing I wear is a long sleeve t-shirt, can't handle the leathers in this weather and all I worry about is the wind burn