I turned out to be caused by the fan assembly air outlet being full of dust so that no air was going through it any more to cool down the system. To get to it to clean it means disassembling the whole system but following the procedure well described in the service Manual under "
Removing the Heat Sink and Fan Assembly",
it took me about an hour to get the job done and since that, the system is running fine again.
Here's the link to the Dell Vostro 3500 Service Manual:
Update: Had to clean it again Apr. 2014, Mai 2015.
Seems like it need yearly maintenance :-)
Here are some images how the fan assembly looked like: