It just so happens I helped a neighbor work through this exact same problem on a GMC pickup, which is the same as a Chevy pickup, regardless of my Dad's insistence that a GMC is a better truck.
We replaced sensor first, then thermostat, checked connections until we were blue in the face. Ended up replacing the guage itself and fixed it.
This, of course, may not have anything to do with your problem, but I thought I'd let you know of our experience. I was very surprised that it turned out to be the guage drifting.
I'm now over my monthly quota for General Motors related comments, I was referring to something about my Vette earlier this morning.
Best of luck,