It never hurts when towing to add an extra cooler, run it in series with the stock cooler in the radiator. Also, if you haven't replaced your radiator in the last 7 or 8 years (or just want to be super cautious) I would replace the radiator if your rig is an auto because of the potential pink milk shake if the radiator fails.
Since you have a 2002, you can monitor your tranny temps via a bluetooth OBD2 reader and the torque app (android phone). Or install a scan gauge. Once you can monitor your tranny temps, if it often goes above 200 degrees while towing, I would add the extra cooler.
I installed a tranny temp gauge in my 97 since it doesn't have one from the factory. I will be towing with it this summer and will install an extra cooler if need be. For now, any towing I have done has been in the winter in Wisconsin so it hasn't got past maybe 170 degrees.