So, the fan is running at ~3900 rpm at idle load, and 41 Celsius, according to Open Hardware Monitor.
It sounds like a jet, and is totally breaking my concentration. I can't get it to go slower using Overdrive.
I know the card is old, but I can't afford to replace it
The problem has been intermittent, and has usually resolved itself by booting. This time it isn't going away though.
I dusted out the fan rotor this summer.
Watch this video of this HD4870 owner and listen to his card before and after he installed is Arctic Cooling Accelero Twin Turbo. Major difference. Not only that but his Thermals dropped by 10C. VGA coolers for the most part are very easy to install.
I solved it by replacing the card with a friends old card (actually slightly better than mine )
As I took out the 4890, I checked the fan rotor for dust. There was almost nothing, so what I think has happened, is that the axle has broken, and the fan is turning only by friction (this explains the relatively high temperatures at low load and high rpm), and it also explains some minor degradation in the graphics I've had while gaming lately.