Hang on now, there is one very big difference between a car radiator and the human body and that is called evaporative cooling. Yes, air hotter than 98.6 can certainly cool you down. That is what sweating is for. Otherwise we would have fatality rates in the thousands every single day it is above 99 degrees outside.
I work in places where the temperature can peak out at 145 degrees, and in that kind of heat if there isn't something to pull heat away, then you would have less than 15 minutes before heat stroke kicked in.
That is why these things work so well:
http://www.homedepot.com/p/Port-A-C...ive-Cooler-for-700-sq-ft-PAC2KCYC01/202221382
http://www.speedlifemotorsport.com/dei-intercooler-water-sprayer-kit/
http://www.uline.com/Product/ProductDetailRootItem.Aspx?modelnumber=S-17096
http://www.pattersonroofcooling.com/
In fact, the last link was tried out by our sister company last August. Inside of their trailers they registered over 110 degrees. The water system only runs for 30 seconds every 15 minutes, yet in less than two cycles the temperatures inside the trailer had dropped to 91 degrees, cooler than the ambient temperature. It worked so well that we are going to adopt the same system at our facility.
While we are on this topic, one must remember that there is a huge difference between "feeling hotter" and "not cooling". Gotta remember that.