Air conditioning in cars in the 1950's and Trucks in the 1960's was almost unheard of except for the Swamp Coolers that were mounted in the passenger window.
Another pretty effective way to stay cooler, was to use the seat cushions that allowed air to circulate behind your back and under your butt. Not many remember these from years ago, but I went on the hunt for some when I was making plans to drive coast to coast in 2007, in my 1937 Chevrolet Pickup Truck. I found a couple of them on e-bay and it was one of my favorite sellers that had them.
I was very glad I had them when I ended up driving in temperatures that topped 100 degrees. I could feel the pleasant breeze behind my back and only imagined what it would have been like without the seat coolers, sitting against the vinyl.