I have a 88' craftsman 16hp mower. Once warmed up after running and then I shut it off to do something, it will not restart until thoroughly cooled off. Today I noticed it's in-line fuel filter was empty. I pressurized the tank to force fuel down the line but it still would not start when warm. Any suggestions?

The engine runs fine while running correct? Then YOU turn it off, or does it die?

The engine runs fine from a cold start until I shut it off at which time it does not want to restart.

Could be a faulty solenoid.