Check the compression before starting with a gauge or try and hold it in with your thumb or finger. Run it until it stops, check the compression again. If the compression is about the same you probably have a good cyl/piston/ring set. I would still rem the muffler and ck them through the exhaust port. If They Are Good, The Hunt Is On! The good thing is, it should be a less expensive hunt.

Such as, have you done any servicing to clean carb and fuel sys to know it is not running too lean?

Good Luck! Please Post Your Results/Solutions.

I would suspect the ignition coil. When cool, it sparks strongly, but when hot the spark is not very strong. I have had one trimmer engine that exhibited this same type condition. It would start and run well until it ran out of gas. When it had to be stopped for fuel, it would never start again until it had time to cool down. I swapped the coil and it runs and starts well now when hot.