I don't think you're low on coolant; usually, that leads to overheating, not overcooling. Same for a blockage in the system.
Since you have a radiator cap, you can check that when you first start it up - if the t-stat is stuck open, you may see some fluid movement almost immediately after you start it up (you may need to have someone raise the RPM a bit while you check). I say 'may', b/c the 5.3L is a reverse flow engine - hot coolant flows from engine through bottom radiator hose (once the t-stat opens), feeding the engine with cooled liquid, via the top hose.
If you put new coolant in recently, make sure you're not running pure 100% antifreeze - get a cheap coolant tester and check. 50-50 (w/ distilled water) is optimal; if you live somewhere really, really cold, you can go to 65-70%, but not past there. (if 'clt' is Charlotte, NC, that's not 'cold'... use a 50-50 mix for that area)
If you have a diagnostic tool (even if just a phone-based app like Torque, etc.), engage that, and see what it reports as the temperature, monitoring from the time you start it up 'cold', through when it should be warmed up (yes, I know it's getting that temp from the sensor (that you replaced) reporting back to the ECM.)
If it matches the dash and never rises, then you know the stepper motor / gauge in the dash is OK. If your diag tool reports a good temp back (somewhere between 184F and 195F or so), then you know the stepper motor for that gauge is likely toast. If needed, take it out on the highway for a few miles to see if the temp rises at all.
Make sure you have the diag tool running at all times when you're driving / testing, especially on the highway - last thing you want is to potentially overheat (anything over 220F, is time to pull over and idle or shut down, until you cool off).
Next would be the t-stat (yeah, it's a bit of work to get to; one of the worst things is getting the fan off the WP) Since yours is an '06, I think you have the revised design WP (which uses a standalone t-stat, not one contained / permanently embedded within a neck assembly.) I see you have an '02 as well, but no V8 for that year, so it must have the I6.
Depending on how many miles you have on the truck, replacing the WP, even though it's not leaking, might be good preventative maintenance.
Actually, since you should have the 2nd design pump, you should be able to get to the t-stat by simply disconnecting / removing the lower hose, or at most, the neck for the t-stat, along with the hose (2 x 10mm bolts). If nothing else, you should be able to tell if it's stuck open from there.
Drain the radiator first -- loosen the clamp where the lower hose joins the radiator, and pull it back. Stage your collection pan underneath, then get a fairly sturdy flat-bladed screwdriver, and pry on the *bottom* side where the hose joins the radiator neck. Once you break the seal, It'll start draining, and you can control flow by moving the screwdriver around a bit. After the flow stops completely, you can unbolt the bolts on the t-stat housing (which is at the other end of that lower hose).
To check the t-stat, assuming it's not obviously stuck open... get a pot of tap water (no antifreeze), along with a candy thermometer (or a probe thermometer -- something that can measure past 200F). Put the t-stat in, turn on the burner, and check to see that it opens. It'll probably start opening somewhere between 130F and 150F, and s/b fully open by 185F.
Removing the serpentine will probably give you some room in that area; if you go in through the top, disconnect the top hose (again, at the radiator) for more room, as well. When reinstalling those bolts, tighten them a couple ft-lb tighter than spec (which is 11 ft-lb, IIRC) -- I originally tightened mine to spec, and while towing, I was losing coolant at the t-stat. Took me forever to find it, too, even though I was losing a pint or so a day.
A couple extra ft-lb when I re-tightened it, along with some blue threadlocker on the bolts, and it's been fine ever since. Use a gasket on the t-stat, not sealant, and the same for the WP, if you replace it (you should get replacements with the WP, and the WP gaskets should be metal surrounded by silicone around the edges)
If you weren't in a hurry to make that road trip, I'd say get a tune from
@limequat, who'll only charge you $99 to remove the fan codes (and you can replace the viscous clutch with a thermal one (like GM did for the last year of the run, anyway). That's basically what I did with my '03 - my fan clutch was going out, and I mailed my PCM to him, while I replaced the WP (preventative), t-stat, hoses, belts, etc. You can reach him via PM here at the @ symbol I mentioned above; his website is
here BTW... if you like getting into the pedal a bit, have him remove (or lower) 'torque mgmt'... it'll wake that 5.3L up.
When you put everything back together, the air bleed for the coolant is done by disconnecting the right side small coolant hose on the bottom of the throttle body (the TB 'preheater' hose). When coolant starts running out of the TB orifice (engine off / cold, of course), and your level in the overflow bottle is correct, the system is full of coolant.
That's all I can think of for now. If none of that works, let's see if others have any addn'l ideas.
Sorry so long... I tried to be thorough.
