I always soak an old white t-shirt in water, then wrap around the neck. Your neck has vessels close to surface & rag evaporating cools them. Just re-wet in washrooms or other means.
When I worked at my local drag strip for 10 years, I would always have a wet rag to keep my neck cool, on really hot days. The hot weather, along with the track surface... would be murder on track officials. Hydration and cool rags were the best way to get through day.
