Don't underestimate the amount of heat the oil removes from the engine...
It is critical... Without it's help pistons would burn up within minutes,
valve springs would overheat, etc...High powered engines often have a an oil
spray directed to the bottom of the piston... The oil cooler is needed where
the oil pan, case, prop hub, and tappet covers, cannot radiate the heat load
adequately...
Denny

Oil doesn't do "coolling" per se;