Good day

I pull a 26 ft travel trailer with my 02 F150 Supercrew 4.6L (this has ford stock tow package on it) pulling up hill from Albany, NY this summerI noted the tranny temp sitting around 220 F, although not for long it sat there for about 40 mins. I dump tranny fluid every year , but I am curious as to what recommendations anyone would make? Perhaps a larger tranny cooler? With the K&N 770 Cold air intake system I can crest a 6% grade at about 50 mph.