Sounds to me, like when the engine is shut down all the heat coming of the engine is boiling the fuel out of the fuel bowl of the carb. Befor taking the carb off ry this. Cut 2 pieces of sheet metal and roughly cut out half the carb base area so you can snuggly fit them between the manifold and carb. Drive around as usual untill the engine is warm, shut down motor and stick the 2 p[ieces of sheetmetal around the carb. Come back in 10--15 minutes or so and try to start up. If it starts easy Then order a carburetor heat shield and install it.