The first thing you need to do is determine if the plug is getting a spark when the engine dies when hot. Coils stop producing current when hot. How do you do that? Take the plug out, use a pair of vice grips and attach the metal part of the plug to metal on the engine. Do not clamp onto the glass or porcelain part of the plug. Attach the plug wire, spin the engine over with the starter. While doing this look at the spark plug gap.you should see spark arching. The second is to determine if the carburetor is getting fuel. Disconnect the fuel line from the carburetor. Careful here gasoline will flash burn when spilled on a hot engine. Make sure you have something to catch the fuel. Got fuel when the engine is spun over with the starter. Yes good it is not a fuel problem. No it is a fuel related problem, look for the fuel pump.
