It possibly can be the coil is going bad. The engine heat may be degrading the coil and fails to provide a spark. To test once you shut down the engine when heated and it fails to start, pull the spark plug and ground the plug to the engine somewhere and have a helper pull the chord to see if there is spark. No spark indicates coil is bad, if you have spsrk it's a different issue. A spark plug tester would make things easier if you have one.

Does it have an autochoke? They had a tech bulletin or recall on some autochokes of a certain model range.