my 2003 2500hd has the 4l80e.
I can tell you the Torque Converter (TC) unlocks in 3td and it creates a lot of heat - so much that I try not to tow in it. I have a 16 pass stacked plate trans cooler (downstream from the radiator cooler) and on flat level ground I run at 165 - 175 consistently (when it's about 90+ degrees outside).
When I pull in 3td gear, that temperature rises up to between 195 - 200 degrees.
Climbing hills it's similar in temperature (sometimes up to 210-220) but it's on a 14mile hill climb, in 2nd gear, wide open throttle). As soon as I crest, the temp drops back down (depending on the gear of course).
I have often lamented about my 4l80e and how it shifts and it's random shift points (both in and out of haul mode). The longevity of the transmission, towing though is a sign that the engineers know what they were doing with this transmission. I've got over 152,000 miles on it, pulling my 5er and daily city driving. I do have the pan dropped, and the filter changed annually and had the fluid flushed. That allows me to have the particulate matter inspected and thus far, nothing has been burned.
I wish I could control the shift points as well as the TC though!