My essential hot weather accessory is a plain cotton bandana. I just get it wet and tie it around my neck loosely. When it feels like it is starting to pick up too much heat, I just take it off, grab it by the opposite corners, give it a few flaps in the air, and retie it on.
The evaporative cooling from waving it in the air really cools it down. When that recooled bandana touches my hot neck, I've been known to give a surprised yelp at how cool it is.
I may try one of the fancy neck coolers cited in this thread, but will still always have a bandana with me - it's a towel, napkin, seat cover, bag for holding "treasures", "I'm over here in the crowd" flag, or whatever I need.