A quick check when the car stops to see if it is the fuel system. Slacken the nut holding the carb inlet mesh filter. If there is fuel in the carb it should show.
If it proves not to be a fuel issue then if the car has a normal distributor with points and condensor, swap the condenser as it may be breaking down when it gets hot.
After that if nothing resolved, check/change the coil as again it could be breaking down when getting hot.