when you say "overheating" what temp does the truck get to? Does it just go up to 230F or so?? If so, don't worry.
Has it got hot enough to go into a safety low power mode??
Yes, LLY does get hot and in some cases will get hot enough to go into low power mode. Haven't had that happen to mine, but I only tow about 11K lbs. and about 19K overall.
However, the fan does come on. You know when!!. And coolant temps have gone up to about 230F at times, (measured with a scanguage not the dash temp guage) but never anywhere near the red zone, and when the fan comes on, it has always stopped the temp rise, and eventually brought it down.
I did install the newer mouthpiece. Yes, it helps, keeps temps from rising as fast on steep climbs, lets it drop quicker. Doesn't keep the fan from coming on.
and use tow haul mode. It locks up the torque converter full time in 2nd-5th gear, which will limit transmission fluid heat buildup and help the radiator temps.