<<Does that engine have a heat riser valve in the exhaust? If so, have you checked if it is working? >> Yes, there's one where the exhaust manifold meets the pipe but as with many I've had this old, it's stuck in the open position.
Kinda off topic, but the 4 banger in my 1955 IH farm tractor runs better with a couple of clothes pins on the fuel line. It was hard to start when hot, the updraft carb sits right below the exhaust manifold, and the exhaust makes a U turn upward right in front of the carb. I put a sheet metal shield between the exhaust and carb, it helped a little, but a couple of clothes pins on the fuel lines also helped, or I thought it did. I had even re routed a new gas line from the tank to get it farther from the heat, didn't seem to help. Don't know what the clothes pins do, maybe provide a little spot of insulation? This is a gravity feed system, so no pressure to speak of. If the heat is boiling the gas out on a downdraft carb, I think a sheet metal shield between the carb and manifold might block some of it.
In and out ( when everything had a carburetor ) of lots of different and strange cars, taught me one thing. When the day is HOT, crank first. Do NOT EVER touch the gas 'til the fifth or sixth spin. Then slowly open the throttle 'til it kicks. By the way the cars that I would have dealt with were using 7 or 8 lbs for line pressure not the 2-3 lbs of earlier carbs. Hot gas is Hot gas.
Holley 94 used on fords through 40s and 50s, Stromberg 97 used on fords in the 30s. Both carbs are 2 barrel design and are the most common carbs used on hot rods.
First thing you need to do is try what Kerrynzl said..........squirt some starter fluid in the carb and see if it starts immediately. If it does, then you know you have a problem with not having fuel. If it doesn't start immediately , you know its not a fuel related problem. I would also get one of those "spark testers" that you hook inline on a spark plug and hook it up before doing the above test. Then you can see the spark as well.