Fears about inadequate cooling are somewhat unfounded. So long as you are towing within rated capacities, GM says that cooling is sufficient and I personally have found that to be true. I towed 2 different travel trailers with my old '03 Trailblazer, one of them through mountains without an axillary cooler. I had 160k on that truck when I sold it, the trans was as strong as ever. I towed though mountains with a '95 'Burb and that truck has 190k on it now, no axillary cooler, and my dad is still towing a TT with it. Trans is as strong as ever. Both of these have the 4L60E as does my current Sierra.
What year is your GMC? In 2006 they switched trans fluid to Dex VI which is full synthetic and does wonders to help in cooling. If you have a TV that older than 2006 I suggest you switch to Dex VI if you haven't already.
You can run the trans up to 220 without damage, but watch the amount of time you do so. Even a bit over 220 for very short periods won't hurt it.