Wearing a hat is one of the best ways to cool down during hot races. Maybe not cool down, but to stay protected from the sun.
I used to run with a visor. I thought a visor was better than a hat as it might let the heat out easier. But before racing in a sweltering tropical 70.3 my coach suggested I wear a hat. But I only owned baseball caps, and I didn’t want to run with one of those – they’re wool.
So I bought an official race hat at the expo the day before the race. This was an excellent decision. At aid stations, I’d just put a few of those large ice cubes in my hat, then put it on tight enough that they wouldn’t fall out. The ice would melt, and as the cubes melted, the cold water would drip down and cool me off.
Despite the inferno I was running in, the ice would usually last until the next aid station. I think I must have stayed cooler than anybody else on that run! Oh, I also set a personal best then, both in my run and in my entire race.