In temps higher than body temp, my main goal is to support the perspiration--drink water and eat well for electrolytes. Use the sweat for evaporative cooling, or you will get hurt. In high humidity, an additional goal is to augment the evaporation. Rest in the shade and look for a breezy spot. If there's no breeze use your cycling speed to make one. If you can't cool off while riding, stop riding. Pay attention to your brain--if you start getting dizzy, it's almost too late--get medical attention.
Friends in Arizona who are avid hikers in the winter become avid cyclists in the summer, because they know how to use the breeze and perspiration for evaporative cooling. Except for periods of monsoon moisture and higher humidity, it works fairly well. But you absolutely need to support healthy perspiration.
Ditto the comments about covering the skin. Look at what field workers wear--no shorts or tank tops out there. I work on a trail crew of mostly retired folks, and we're all in long sleeves, trousers and wide-brimmed hats. Younger people who come out for a day are usually in shorts and tank tops and ball caps, and suffering by the end of the day.