anaheimxj,
The reason you install the Aux cooler is to get heat out of the ATF. On my 88 XJ you can tow up to 2000 lbs without an aux cooler but my owner's manual says with the aux cooler you can tow up to 5000 lbs.
Lets say our XJs weight 3500 lbs, with a trailer attached engine, transmission, and rear axle are moving more than two times the normal weight of the vehicle.
For most people who never tow the factory set up will meet their needs with no problems. If you are one of the few who tows you will need a larger cooler because of the larger load on the drivetrain. Also keep in mind my 88 XJ says if you tow you have to change the ATF every 15,000 miles, if you don't tow it every 30,000 miles.
Heat transfer is more of an art than a science. You can calculate what size heat exchangers you need for the most extreme conditions but you have to do tests to verify you choose correctly. I am more than willing to say the AMC engineers who designed my 88 XJ spent the time to figure out what aux cooling was required. Remember they sold the vehicle and said if you have all this equipment in the owner's manual then you can tow up to 5000 lbs and be covered by the warranty.
Also keep in mind winter and the engineers took that into account so the transmissoin fluid does not get too cool in winter. It is a balancing act. The solution provided it the best solution for the north american market. If the XJ was designed for a different operation temperature range the radiator and trans cooler would be different sizes.
We all need to keep cooling system maintenance in mind. If you plan on towing and your XJ more than 5 years old I would replace the radiator, radiator hoses and install an aux cooler if you plan to tow over 2000 lbs. With all that you should not have a problem.
If you are worried you can install a temp sensor in one of the trans cooler lines and monitor it. I see GM now has a trans fluid temp gauge on some of their trucks.
If you plan to tow over 2000 lbs then get an aux cooler, the OEM cooler is 48 sq in., and change the ATF fluid every 15,000. With that your XJ should run just fine.
Martin