The oil cooler fan was on after I parked and shut down the engine.
This a common error by many installers of external oil coolers. The installer wired the fan to a constant hot wire that is controlled by the sensor that causes the fan to come on at whatever temperature the sensor is designed to come on at. I know that is confusing so here's another attempt. If your fan controller is a 180 degree sensor switch and the power wire that it controls is constantly hot your fan comes on when the oil gets to 180 degrees and will run even with the engine turned off. The fan will turn off when the oil goes below 170 degrees, IIRC. If the oil sensor switch is a 190 degree switch the same thing except the oil will be hotter before it turns on.
The problem with this is you are only cooling the small amount of oil in the cooler. The oil is not being circulated through the engine so there is no real benefit to having the fan turning when the engine is off. Have it wired so the fan shuts off when the car is off.
And I'm in agreement with the other guys. Find out the real temperature of your oil and its most likely a faulty oil temp sending unit.