I used to tow with an Omega 2.5 auto, but sold it because I only managed around 18 mpg. that was mainly due to the autobox changing down when it saw an incline. If I could have held a gear it may have been better.
As regards the oil cooler, never needed one, and a Vauxhall mechanic told me if I had fitted one during the warranty period, it would have invalidated the warranty.