Mine didn't come with a cooler.

 

I wouldnt do it. Only reason I would take mine off is to put something better on. The factory oil cooler is really an oil temperature stabilizer. To make it a cooler you have to put on an adapter that will be oil to air instead of oil to coolant. Then you have to have a thermostat to keep it from overcooling.

Im guessing a good temp for motor oil is 180-210 degrees.

 

for a street car it needs to get hot enough for condensation to boil out. otherwise you get engine oil spiked with a bit of sulfuric acid.