The Tilley's look good, but hats are something I never buy without trying on.

A basic boonie, in tan. It isn't going to absorb heat due to it's color, and it is versatile. If you really NEED it to be waterproof, you can find them without the ventilation eyelets, but you will miss them when all the steam stays in. And, if you don't mind being a fashion outcast, pin up one side, and with that part of the brim and a bit of doublesided velcro wrap through one of the loops, you can carry a tinned PSK without much trouble.