vapor lock seems to me the cause of this. When too much heat is transfered to the gas line or fuel pump the gas will boil. this causes a void of fuel replaced by air. The fuel pump cannot pump air so the fuel flow stops causing the engine to stop. after sitting the fuel cools down and the air returns to the gas where it came from and everything works again. check to see thet no fuel lines are too close to the exhaust pipes or manifolds, a old fuel pump that is just getting by could also cause this as the rubber diaphragm get old and don't pump effectively.

This same problem plagued me and my 73 for months. I forgot to check the obvious - the fuel filter at the carburetor was so full of junk and floating junk that the engine would starve for fuel. Somebody used Teflon tape on the fuel line threads and it was disintegrating. When it started up again the carburetor bowl would fill and when that was depleted stall again.

Don't miss the inexpensive fuel line filter fix

There are a lot of great ideas here but too many unknown variables. What kind of motor (bb-sb), intake stock?(steel-alum.), carb (roch-holley-other). I have a 68 327-350hp with stock setup. The right carb is a big variable because some come equipped with heat operated bleed-off valves. There was also three gaskets between the steel intakes and the carbs from the factory. One steel heat conductor between two fiber gaskets.
Supper's calling. I'll be back in 15.

Also, do you foul plugs frequently? I am going through the motor compartment now trying to get everything corrected that has been swapped out over the years. Sometime along the way, someone crimped off the fuel return line and just ran a line from the pump to the carb. I think the carb is running fuel into my intake when I get it hot and shut it off for a while.When mine gets hot it turns over slow and takes a while to fire. I have a few variables that I am going to have to isolate to fix this problem. You really shouldn't rip off your fuel pump and replace it unless you know it is faulty. The other parts should be held onto as well, especially if you have the right part numbers and dates on your original equippment.

I had a similar problem and discovered it was the wire that runs between the coil and the distributor. I only discovered this after I replaced everything else. Good luck.

I had that exact same problem with my '81 recently. Turned out that the choke was staying on and the car wouldn't idle once warm.