When I still had the auto in my dually towing at 30k gross I regularly sustained 250-260 on hills or in construction traffic with 3 trans coolers (one even had it's own fan) in series for years and 30k miles but when I took a wrong turn onto a narrow road that after 10 miles of no place to turn around turned into another 10 miles of red dirt switchbacks with STEEP grades in the smokies the gauge buried over 300 and the trans boiled over with a huge smoke cloud.... Luckily the truck didn't catch fire.... I was still able to drive to a campground after getting a case of fluid but the trans was junk and the rest of it's service life was driving onto a trailer for the ride home and driving into my shop for a 6 speed manual swap. I was in a bad place where had I stopped I likely couldn't have started again and no help was available.... You can't exactly put the truck in park or use the e brake on a steep grade with that kind of weight.... I was climbing that hill at full throttle with a modified turbo diesel at full throttle and 3-5 mph....
The point of all this is that while the 240-250 now and again isn't good for the trans and you certainly shouldn't intentionally push it that high, with a fluid change, the trans won't likely be harmed BUT add 50 degrees and it will be done RIGHT NOW.
In closing I'm SOOOO much less nervous towing with my manual now.
