I'm curious. Isn't the breeze you get when biking enough to cool you down? I live in Denmark and we don't often have that kind of weather, but the breeze that you get when riding your bicycle can be really nice in the summer.
I've only experienced Dallas summer heat, but no the breeze doesn't help. I would leave work and it would be ~105 F (40.56 C). I'd get in my car and roll down the windows until the A/C started working. The air that came in while driving would feel like the same temperature as the air in the car, like a hair dryer or something. It was like an omnipresent inescapable oven. Imagining THAT with 80% humidity sounds unbearable.