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Don't get a hat that makes you hotter than you need to be. An outdoor hat is supposed to cool you down and protect your eyes and skin from the sun. A straw wide-brimmed hat that has holes for ventilation is a good choice.
My personal choice is a Brooks HVAC Infiniti Mesh Cap. It's a runner's cap, but style wise it is halfway between a regular runner's cap and a baseball cap. Very light and breathable. Mine is white, for maximum light reflection, but here's a green version if you want it to look more outdoorsy.
