Will it always restart immediately? If so, that argues against it being a heat-related. But if it requires a cool-down period, it may sell be heat-related. Both my failures on my current Onan 2800 required at least 5-15 minutes cooling in summer before they'd re-start (fuel pump, voltage regulator).
Another thing often overlooked is the spark arrestor being plugged, but your symptoms don't match mine when that happened (run fine no or light load, chug down and die under load).
Good luck with it.
Jim, "Trying to understand the behavior of some people is like trying to smell the color nine."