Brett: I wear mine outside of my hood. Sorry if I misunderstood and you were talking about a SA visor.
Yes, the Sunday Afternoon is hotter than some other hats. Again, though, it's made of spf 50(?) (maybe 30?) fabric. It's protecting the top of your head from the sun, as well as your face. That's a trade off I'm willing to make. But I hike cool! Clearly, this doesn't work for you.
I also have a Solumbra shade cap. It has an spf 50. It's cooler than the SA hat. It has a very prominent front brim--4 inches I think. It uses a neck drape. It's great in mosquito season. And it fits under a hood.
Also, Simms makes a terrific visor--four inch front coverage. Excellent rain/snow protection for your eyes.
Sorry if I've gone off topic here.