The disk SMART signaled for a while already that the disk is about to die. When it refused to upgrade to Mountain Lion I decided to replace.
The repair was almost uneventful. I bought a 2TB 3.5 7200 data drive and the instruction sequence on the iFixit site was almost perfect. The only thing I had to improvise was attaching the temperature sensor plug. The original disk (Hitachi 2TB) and the new disk Seagate 2TB have a slightly different slot for the plug and I had to break the slot frame and fix the plug with a drop of glue (fortunately the pins and pin distance where the same). And I thought naively that the drives are completely standardised - and was proven wrong!
Show the details of the drives in a photo - perhaps I could have avoided the hassle by selecting another drive or could have ended worse with an unusable temperature sensor and had had to put up with the noise of a permanently running fan.