To add to Al's explanation. The fans on modern cars are for cooling the couple of gallons of water in the front mount radiator. In modern cars there is more coolant in the radiator than what's in the engine. When the car stops moving there is no airflow thru the radiator so heat builds up in radiator and the fan comes on. That's different than a fan on an oil cooler which holds only maybe a quart with the engine having the bulk of maybe 3 quarts.
This is what you have - there is a remote oil cooler which adds to amount of oil in engine and cools it. Often an electric fan is added to increase air flow thru that oil cooler. A thermostat is added to route cold oil past the oil cooler and could also trigger the fan to turn on.
The key is does the fan turn on when the engine warms up to 180 degrees. If it doesn't and the cooler is out of the main air flow - the cooler doesn't cool much at all.
