I just bought a used 04 Suburban but it does not have a tow package.

For towing less than 5000 #'s do I need to put on an external trans cooler. I was told if I keep the fluid clean and don't go overboard on passing & downshifting I will be fine. It has a trans temp sensor but in my mind if the trans gets too hot it is already too late. Thanks for any help or direction you can give me.