Here is some more info,
I shifted the computer to the AC-room and now I have:
CPU temps: IDLE-33c, LOAD-46c,
CPU fan: IDLE-1250 RPM, LOAD-1900 RPM
At 1250RPM the fan is inaudible, though under load it can be heard.
I guess that means I need a CPU cooler which can handle the load with the
fan...