My 1994 Cavalier was doing something similar yet different for a long while, and still does some things intermittently now. Since my car has many electrical anomalies - including only portions of the electrical system working depending upon how cold it is outside (I really should post that here) - I have chalked it up (probably stupidly, because I have no basis for this and am not generally a total fool) to being more likely an electrical issue than an actual overheating issue.
Mine would heat up if and only if I got directly onto a highway within half a mile from starting it up. Before three miles on the highway it would be close to the red zone, or would spike into the red zone, then would back itself down cooler. The “Check Engine” light would then be on.
If I got back onto the highway after parking but when the car was still warm, it would not say it was overheating at the predetermined two- to three-mile point.
If I started driving on city streets for a while, then got on the highway (or didn’t), it would not show overheating. We do not know whether the car actually overheated, just that the gauge said so.
I do not know what I or my excellent mechanic (who couldn’t find anything wrong) did, but nowadays only sometimes if I get immediately onto a highway, the temperature gauge does not go up any higher than it should, but the “Check Engine” light comes on at the exact same point in travel the temperature would have spiked.
I note that only one thing has changed since it does not show overheating on the gauge but the idiot light does come on: a groundhog chewed my wiring harness (and various other things), and my patient mechanic reconnected the wires.
The temperature gauge seems to work just fine, before and after the groundhog, but it no longer does that spiking thing.
Just throwing this into the mix - it really is neither an answer nor a solution. My car only has about 87,000 miles on it, and I still rely on it.