I am having the same problem with my 2006 Silverado 2500HD LBZ. It will heat up at anything over 10 pounds of boost. I live in the Phoenix valley area and driving up SR87 to Payson, the speed limit is 65mph. There are three 6% long grades. I can't maintain 65mph going up the hills with out slowing down to keep the boost under 10lbs and keep the coolant temp under 200. If the boost goes up to 12lbs or more for any length of time, the temps will go up over 212 degrees. I never hear the fan clutch cut in even when I first start it up after sitting overnight. It has been up to 235 when pulling my travel trailer once so I had to slow down to about 50 to keep the boost down so it would cool off. I read some posts about the Hayden 2850 fan clutch. I checked Ebay and they had one for $91 and change. I then checked my local OReilly's and they listed a Murray fan clutch with the same part number, 2850, so Murray must get them from Hayden. The specs on the Murray were exactly the same as the Hayden and it was only $74.99. I will pick it up on Monday and we will see if that changes things. Oh, I changed both thermostats last week and that didn't change it. I checked the old thermostats by putting them in a pot of boiling water and they both opened perfectly.
Those temps actually sound about right when pulling a good load. These engines really generate heat when they are working hard. I'm pulling a 14k lb fifth wheel. In the west TX summer, I run 210 just going down the flat highway at 65 mph. Pulling any kind of significant hill, I will hit 230-235. At this point, you can really hear the fan fully engage. The fan starts roaring, then temps start coming down to about 215-220 even if I am still going up the grade. I have read somewhere that one of the thermostats is not even fully opened until above 220.
Also keep in mind, when it is 110 outside, the air getting to the radiator is probably 150 or higher. It is being heated by the transmission cooler, AC condenser, and intercooler before it ever even gets to the radiator. The higher the boost, the hotter the compressed intake air is.
Clean your cooling stack by REMOVING it. You cannot clean it well while it is still sandwiched in there.
I am also considering the Hayden, but IMHO temps up to 235 are fine as long as they cool back down once the fan engages. Temps of 210 while towing are completely normal and nothing to worry about.