When PTO is engaged the motor gets hot quits charging and PTO shuts down.
This write-up is unclear. This is the way I read this...
1. Everything is fine. Engine will run and idle just great. No problems starting or running.
2. Then PTO is engaged.
3. Something gets "hot". Engine gets hot ? PTO gets hot ? Belts get hot ? More details needed. How do you know it's hotter: measured temperature, smell, feel, crystal ball, what ??
4. Battery stops being charged. Did the battery have an ammeter on it before the PTO was engaged to insure charging was present at Item #1 ? And then an ammeter was connected again after Item #3 ?? Exactly how much was the charging before charging ended ?
5. The PTO quits. You mean the engine kept running, but the PTO clutch dis-engaged ? Or do you mean the whole mower, engine, PTO, and all quit ?
We only know what you tell us, but more detail is needed to understand.
Hope this helps.