Thanks, Pat!
My mechanic friend told me that he tested the gauge and it was ok. It's the Remote temperature sensor that's bad (finally got the name of the thing, thanks to your link and a very interesting read). I found it in the catalog alright, part No. OEM-90164163200.
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I'm trying to get the correct part from the USA because I cannot find it in Europe. I had some trouble translating the name of the part from German to English, hence this post.
I guess I'm pretty much hopeless when it comes to cars and I can see I have an interesting road ahead of me! But the 911 is such a lovely thing that I am more than willing to learn. This place looks like a great spot to start, by the way, a lot of very useful articles. And this forum is very lively, too.
Thanks again!
Jure