I immediately thought of creating a cat cooler to give them a cool spot to lay on. I googled the concept and found that I wasn't the first to think of a cat cooler. One other person on the internet had the same idea. His concept is pictured below, and you can read about it HERE.
The above idea isn't thought out well. It relies on water evaporating off a towel below the aluminum cake pan to cool the kitty.
I have a better idea. I call it CCCC, or the Cosmological Cabbage Cat Cooler or C4. It works on the simple principle of siphoning off a bit of cool in your air-conditioned house and transferring it outdoors to cool a platform that the kitties lay on.
Essentially you get some copper refrigeration tubing and create two radiator-like networks. You fill the tubing with a liquid like anti-freeze which carries cold well. Then you put half the thing indoors, and the other half outdoors. If the indoor unit is higher than the outdoor unit, you do not need a pump. As the liquid cools, it becomes denser and pushes itself outside while the outdoor-heated liquid is lighter and ends up inside to get cooled. The process continues by itself.
Only cat-lovers have an interest in this idea. We are not exactly cat-lovers. We just got roped into feeding feral cats and cannot bear the thought of cutting them off and starving them. But as long as they are mooching off us, they might as well be like me -- cool!