Well, maybe the motor is a politician!
(naw, jes kidding!)
What you describe is called "Dieseling". It happens when the motor is so hot, that the engine ignites it's own fuel, and keeps on running. It is most likely caused by a LEAN condition (Lean = HOT).
It is STOPPED by pulling out the choke all the way. This floods the motor with gas, and cools it at the same time.
It is fixed by solving the lean condition, which is usually fuel delivery.
Gray fuel hoses can dissolve into the fuel, and stop up filters.
Filters can be clogged.
Carburetors can have gunk in them.
Tank can be real low on fuel.
Fuel select valve can be clogged.
Be sure you don't run it again, before fixing it. Lean runs with a new motor can score the cylinders, and overheating the rings causes them to loose their tension, resulting in a weak motor.
I hope this helps.
Nate