Transmission
Oil coolers are used in many OEM towing applications, go look at a few new vehicles and compare to what you are using and how they are plumbed.
If you are using a conventional
oil cooler, be sure to mount it so the body is sandwiched and not located by the bottom or top end plates alone, Earls has in their catalog some examples of how to mount them, vibration will definately shorten their life dramatically.