220 degrees is not a problem for the ATF. The fluid has a flash point of 379 degrees. I expect the ATF temperature to be 100 degrees above the ambient temperature where I am driving with my truck. If it is 100 F degrees outside the cooler is less effective and the ATF will run hotter.
If you have tow/haul with your vehicle be sure to use it with a heavy load as it is designed to minimize wear on the transmission and keep it operating cooler.
What would conceivably help with long grades is adding an extra fan or a cowl to most more air past the transmission cooler's fins. When going up a steep grade the transmission is getting hotter and more heat is going into the fluid but there is a lot less air passing through the cooler to carry off the heat.