Erratic coolant temperature

[AlHeart]

When I'm driving uphill on the highway, the temperature needle starts moving to the right of centre. It goes back to the centre fairly quickly when driving level or downhill and in city traffic or idling. When going uphill, I'm not taxing the motor - most of the time it is 1900-2500 RPM. This just started a few weeks ago. Before that it was normal in these conditions. I should add that I'm driving in winter temperatures, below freezing.

My 2004 A8L 4.2 has 210k km.

I have no coolant leaks, both fans are working fine and so is the heat. I originally thought it was air in the system. I got it to operating temperature with the coolant expansion tank cap off. I'm not sure if that can help get some air out, but that didn't help. I tried the bleed procedure with vcds but couldn't figure that out. I will try that again.

Does this sound like a partially open/closed thermostat? Or could it be the coolant temperature sensor? Or something else?