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Boonie hats are hot as well. There is a model made by Columbia (I think) that has mesh in it around the crown and is a lot cooler. You can also get a canvas hat and keep it wet (requires extra water or local water features.
The ideal hat for arid, hot environments has already been developed and meets all of your requirements except for crushable (arguable I know). There is a reason people who work outside dress a certain way for the area they live in. Pic related.
