220 is too hot for sure. I have the exact same truck as you and I added a cooler and trans temp gauge last year off ebay. Best money I spent on the truck. I towed 6000 lbs today at 75 degrees outside and it pegged at 150 degrees and never got hotter. 220 is approaching pull over to the side of the road temp. You don't want to be spewing trans fluid on the ground and overheating a very expensive trans so get yourself a good cooler and gauge. by the way I know this truck inside and out and have been doing road service and been a mechanic 22 years. 220 is too hot, and the little cooler you will see on the front of the radiator at the lower edge is NOT a trans cooler, it's a power steering cooler on the F250.