these generators tend to be hard to start when hot. Problem is
they have a mechanical governor system, and governor spring holds throttle at wide open position when not running. when engine is cold, choke mechanism richens up fuel mixture sufficiently to aid in starting.
But when choke is off (as in hot engine), the wide open throttle causes there to be very low vacuum in carb, and fuel is not being drawn in
adequately to start at low cranking speeds. If some of carb jets/ports are partially varnished from long periods of not running, this makes problem worse. a new carb or really good cleaning may help, but only other fix I can offer is to manually close choke by hand if you need to restart a hot engine. hope this may help