temperature will always get hotter faster under load than water temperature because there is not much heat exchange unlike the coolant which has a radiator. It all ends up being air cooled in the long run. But the radiator has more surface air than than air cooled oil cooler. Liquid always cools faster than air because it is dense. When you burn your finger do you use air or water to cool? Square inch to square inch water will cool faster than air. In racing they are going WOT for hours they are using water cooled oil coolers because it is more efficient easier to install .
When it comes to intercooling, water cooled intercooler work best for drag racing becase you can use ice water. For street they end up being heat soaked. You don't want your boosted air to become 180 degrees. With oil you do want it to reach 180 degrees.