I'm a little suspicious about the fact that it "won’t crank" until it cools off. Something like that would make me wonder if there was an electrical problem in addition to the fuel problem. If it won't even crank, I wonder if some electrical connection is opening when it heats up.
About the fuel problem . . . I don’t know about the older trucks, but my '53 has a spring just below the carb. This spring changes the flow of the exhaust gases in the exhaust manifold as the engine warms. If your truck has one of these is it missing or broken or overly tight. My factory repair manual says that this could be a cause of poor running or low gas mileage.
