A few years back I had a similar problem with my Onan 4K.........it would run fine for about 20 minutes and then shut off and would not restart until it had cooled back to pretty much ambient temperature........it was not fuel related because I could spray starter fluid in the carb while pushing the start button.....and nothing.......not even a pop.......
The spark plug was getting spark........but apparently it wasn't enough....
In the end I replaced the magneto mounted behind the flywheel.......about $80.....it has not hiccuped since.......
You may have a similar issue......Good luck!
