I have a Honda 300 1996 model. I need some help with a problem I’m having with it.

The machine will crank fine and runs well, until it gets hot and is idling. It does not run rough but just cuts off. It will crank back up after 15 or 20 minutes. It mostly does this at lower idle and not so much at a little higher rpm.

It charges the battery fine so I don’t think it is the stator. I suspect it is the rectifier but I am unsure. There also seems to be some other box that can cause this. Any ideas?