Denali has the Mac Daddy cooling system for its 6.2L. If the radiator has no history, replace it simply due to its age. All radiators are prone to collecting the equivalent of brake dust on the interior and exterior surfaces. When it starts, it grows like barnacles on a whale.
Start with a flush and Rad replacement, OEM only, they have a lifetime guarantee now. If you want to know if it was part of the problem, weigh the new and old one after it’s dried out in the sun for a week. If it’s significantly heavier, that’s not good.
Replace the coolant reservoir too. Our 08 Denali would overheat at idle on 100* days with the a/c on waiting for the kids to come out from school. In the months following we found both the Rad and Exp tank had cracks that wept and caused pressure loss which led to the overheat.