Is there any water in the oil???
My oil cooler failed and allowed water into the coolant but no coolant made it into the oil. As mentioned above, the S oil cooler is about 2x bigger than the base and bolts right on. The oil cooler is on the drivers side (USA) of the engine kinda of under the intake. Easy to take off and check/change.
That is the new S cooler installed:
Oil on 1 side, water on the other. It was very easy to apply a small bit of air pressure and see the bubbles. I recall the relief when the bubbles showed.