If your MD22 setup is the same as mine, the heat exchanger is a long assembly runninh the length of the starboard side of the motor.
Most of the heat exchanger is for cooling water, but the aft-most 6 inches is an oil cooler.
While I'm not totally positive, I do believe a good amount of oil will stay residual in that oil cooler. It would require disconnecting and bleeding a hose (or both hoses) circulating the oil through that cooler to get everything out.
Of course, your mileage may vary and I just know about my particular setup :)
SM #209, Adagio