AFN Temp. Problem?

Hello, for some time now, my 1998 Passat AFN has been exhibiting some strange behavior:

The glow plug indicator stays on for a long time when the engine is cold (like in the middle of winter!).

And sometimes, the idle speed is also slightly increased, just like during a cold start in the winter!

I think there might be a faulty temperature sensor. But which one is responsible for that?

Thank you for your help.