[HELP] Temp Gauge Higher but Coolant Temp Fine

Hi, I need some help diagnosing my E46 [320ci, 2000, EUDM]

As title states, I've recently been seeing my temp gauge leaning a little (but noticably) to the right from center position.

I've already checked engine temp through the hidden dash test menu and OBD scanner.

I can confirm that temp climbs to 96 C upon which fan kicks in and from then on temps keep between 94 to 96 C.

HOWEVER

On multiple occasions I drove my car with needle sticking to the right. Parked, did my groceries, came back and on the way home my temp gauge was steadily in the middle with temps ranging 94 - 96 C.

Anyone has any idea what could be causing this? Where would I start diagnosing what's wrong?

I'm afraid that on day I'll overheat the engine. Seems to me like something's on its way out.