I feel like most install a WDH when getting up there weight/size wise as it just flat out improves safety even if you aren't trying to max it out. I can't say I've seen too many posts they upgraded the cooler, it should be sufficient unless we are talking long uphill grades and to determine the true need you're going to need a gauge/tuner to read out Temps and see how it performs.
I've personally never needed to tow beyond 5k lbs in my 2003. It handled it no problem in stock form aside from the old 5.4's lack of power while winding up the road from the lake, no issues temp wise. It's not a 3rd gen but you should be equipped to handle as much as mine being the same ratings and considerably more power and a couple extra gears to help out.
