By “it should not overheat”, I mean it is not acceptable that it overheats, not that it will not occur. If the transmission is overheating going up hill on a paved road on the cars own weight, it should have been not rated to tow 6000 lbs, because it will overheat with that on a flat road with stop and go traffic.It will if the transmission is constantly shifting. I got the one in my 99 lx470 pretty warm one time. I was on a gravel road with a speed right between 2 gears. I just moved my shifter down which solved the problem. The lx470 has a decent sized tranny cooler.
If it is an excessive shifting issue, it will be a rather easy software fix that can make the transmission stick to a lower gear above a certain fluid temperature. Tow/haul mode or manual mode may also work until Toyota comes with a solution.