Since illness from heat has come up, please note this can be a very serious condition. Heat stroke, the most severe form of heat caused illness, has about a 10% fatality rate. Some helpful sites on what to watch out for etc.:
Heat Exhaustion and Heatstroke: What You Should Know
Heat Stress (NIOSH site)
Safeguarding against heat hazards (OH&S site)

I have never used one, but cooling vests are sometimes used to prevent workplace related heat illness. Also, I recall some cyclists in RAAM have used some sort of cooling vest while crossing the desert and other hot areas in this coast-to-coast race across the USA. Some cooling vest vendors are Cool Vest, Core Cooler, and TiMountain. Since these seem to work by evaporation, I would think these would not be as effective in high humidity, low airspeed conditions when evaporative cooling via sweating is also less effective. I wonder if anyone makes an ice-based cooling vest? Edit: The OH&S site mentions cooling vests with ice packs, so there should be some available.