I just started having this issue as well. 2016 Silverado 1500 LT 5.3L
This won't be your standard answer, but may point you in the right direction to the cause.
Driving under normal RPM, would run at 210. Stepping on the gas or going up a grade, it would creep to 250-260 needle pegged. I would let off the gas to drop the RPM and it would cool back down to 210.
Took it in and they did a block test, and it failed. Exhaust gas in the cooling system.
Either a head gasket leak or a crack in the block.
Vehicle overheats:
**FAIL BLOCK TEST** --REFFER TO ENGINE SHOP OR
DEALER
*FANS ARE TURNING ON, FOUND NO EXTERNAL LEAKS*
Got a couple quotes to replace the head gaskets and machine the head if needed. $4-5k
Got a quote to R&R the engine and replace it with a remanufactured Jasper AFM Delete (no more dropping to 4 cyl.) engine (not a rebuild) with the Installation kit. $11k
Installation kit includes new water pump, fuel pump, thermostat, all filters, plugs, belts, and hoses.
I would rather replace the whole thing than nickle and dime the rest of the old parts after doing a head gasket\machine head.
Transmission was replaced 2 years ago (under warranty), so with a new-ish transmission and a new engine, i'm getting basically a new truck (I like my truck) for 1/6th the cost of a new one.
Dropping it off Monday and should be done by Friday.