Have you checked the carb before trying to start the hot engine? If you're seeing any seepage or hearing any hissing or bubbling noises, the fuel could be boiling in the float bowl after you shut down. That could cause these kinds of issues.
Do you have the correct carb base gasket? Some of them are made of thick, insulating material to limit heat transfer from the manifold to the carb. Make sure yours is the correct one for your year/engine.
Is your fuel feed line (from the pump to the carb) routed correctly and not close to any hot engine or cooling system components?
If Cliff found the carb to be working properly, I'd check the fuel pump, too. It might be putting out too much pressure and overcoming the needle/seat shut-off. This should be evident all the time, though; it would be running rich and loading up all the time.
1968 Pontiac GTO
1983 Pontiac Bonneville (G) wagon
2008 Pontiac G8 base