There is a really common problem with these cars, where the modern gasohol with a lower boiling point begins to do just that when the car is hot. Do you have a gas smell? That's a
part of it. The
carb should have a spacer plate under it, and I believe coolant runs through it. If an aftermarket
carb, make sure there is a space plate under it as opposed to mounting directly on the manifold. My 64 has an Edelbroak manifold and
carb, and starting was a mess when hot. Then it had a tendency to stall when backing out of a parking space, and there is always some nut who flies past, making me stop -- and stall -- and crank and crank again to start it. After driving half a block it smooths out. Adding a spacer plate helped immensely, but I still get it a little at times. The solution may be fuel injection.