An oil cooler is a another way for the overall engine to shed heat generated by combustion. When oil comes in contact with engine bearings and parts like the cylinder heads, as long as the oil is cooler than the metal part, it will take on or absorb heat from that metal part. Now if there is some way for the oil to release this heat to the atmosphere (oil cooler), it can go back in and pick up more heat. The oil can do this over and over again in a big loop fashion. Any part that the oil comes in contact with, heat from those parts will transfer to the oil. On late model engines there are oil jets that spray oil to the underneath area of the piston and skirt in order to help reduce heat.
The only issue you have with an oil cooler is that the bike needs to be in motion for the oil to dump it's heat to the atmosphere. It really does not do a whole bunch of good if your sitting still in traffic and that's the time you need it most.