I would suspect a failed coolant temperature sensor. Just guessing though. The reason being that it controls the fan. When the engine is hot or overheated, that fan should be running constantly until the engine cools down some.
A bad sensor could/should throw a trouble code, and the service engine light should be on. Is it on? If so, get it scanned. AutoZone, Advance Auto, and O'reilly Auto Parts can all scan for codes for free (if you can get there).
It could also be a bad electric motor in the cooling fan. To test it, I would pull the fan, and run a hot wire to it. See if it starts and stops the same way that you are observing. If so, replace the fan. The brushes inside the electric motor are probably worn out and when the fan motor heats up, they are not making a good enough contact to run. Or something to that effect.
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Wednesday, September 6th, 2017 AT 6:53 PM