@Uncle Phil
Unless it is a short errand, I usually ride in a one piece Aerostich R3 (unlined) suit... in Texas no less. What I have found to work for me is a couple things.
First, I wear jeans and a long sleeve T-shirt under the suit. I know it sounds counterintuitive, but the the long sleeves work as an insulating barrier from the heat. The hot sun bakes down on the R3 suit and the arms are at a perfect angle to soak up all that radiant heat. If I wear a short sleeve shirt then my forearms are in direct contact with the inside of the suit material -- which gets very hot from the sun. But if I wear a long sleeve shirt then the fabric of the shirt prevents direct contact with the (hot) suit and allows air to circulate and cool me off (evaporative cooling). Also, the 'STich is designed with vents in the armpits and at the back. I have found that, while riding, the air enters the suit through the neck area (and up the sleeves if not zipped) and vents out through the armpits/back. But, in doing so, the suit inflates from the air pressure and keeps the inner surface of the suit from direct contact with you -- thereby creating a kind of
bubble insulation, if you will. I have found it to be pretty ingenious how it works. Also, it kinda makes me look like the Michelin Man when I'm riding...LOL.
The second thing that helps me is that I keep a tank bag with a hydration bladder inside so I can drink water while I am riding. When the temps get above 90 (especially in the 100s) always, always, always HYDRATE! I use a 2 liter bladder and fill it as much as I can with ice and then top it off with cold water, wrap it in a small towel for insulation, and then stuff it in the tank bag. I have found that it will provide me with at least three hours of (n)ice cold water to sip on while I ride, at which point, I am ready for a gas station to empty one tank and fill the other. At the pitstop I just take the tank bag inside the station with me and ask them if I could pay them for some ice/water from the fountain drink dispenser to top it off for the next leg. They almost always tell me to go ahead without charging me anything for the ice/water. Being able to drink on the fly without stopping is a great time saver at pitstops to quickly get me back on the road again.
As always, YMMV. But that is what works for me.
