You will find Yellowstone a great deal higher than 5,000'... More like 6,800' to 8,500'{ I just spent a week there}. You should be a lot more worried about your transmission fluid temps than the engine coolant temperatures. Hopefully you have a gauge that displays trans temp {like a Scan Gauge} and if not you NEED one!
Your engine/transmission coolant temps should never exceed about 225 and then only in extreme heat and under a heavy load. So long as the temps cool back down as soon as the load is removed you should be fine. Your trans temps will be 12 - 20 degrees higher than they should be {and not in a good way} unless you religiously utilize your Tow Haul function. A Scan Gauge will demonstrate this quite clearly and if you are not using TH your are slowly but surely cooking your transmission {needlessly}.
We are In St George, Utah wrapping up a three week trip that will come in at around 4,000+ miles. Climbing the 8, 9 and even 10,000' passes we have encountered the coolant rarely saw 212 and the trans 206 and I am fully loaded and towing a 2,200# 10' X 6 ' {8' tall} cargo trailer with my 2012 E-350 V-10 24' Class C {I have my Indian Springfield - 875# and some misc gear in the trailer}.
I have had this rig for nearly 7 years with 62,000 miles on it and live in southern Arizona RVing year round the whole time. As soon as I bought the coach {used with just 6,208 miles on it} I changed out the oil, trans fluid and differential for full synthetic and yes, it helps a lot!
Keep good fluids and the temps in the proper range and your 6L or my 6.8 V-10 will last longer than we will.
As always... Opinions and YMMV.
:C