I recently sold my 2007 1500 with the same specs but with 3:42 gears. On 90 plus degree days, the trans temp would hit 200-210 all the time and that was with new fluid at pulling over 5k lbs. I had the tow package with the small factory trans cooler and no matter what I did (dropped to 3rd gear, slowed down)that trans temp really didn't drop much. The factory trans cooler is just too small. 200-210 seems to be the norm but if you are concerned, I'd upgrade to a bigger cooler...replace the existing cooler, don't add anotehr in line. You can add
thesecooler line adapters and keep the old lines then use a Tru Cool or similar cooler like
this B&M. The factory cooler is a tube and fin design while most aftermarkets are stacked plated designs which have more tubing inside the cooler to minimize their overall size.