Anyway, I've finally got round to investigating, and the problem is the fan for the "Canterwood 875" device. That's a small square bit between the main CPU and the graphics card. (Former flatmates may remember it as the bit that puts disco lights on the ceiling, since it has red/green/blue LEDs inside.)
However, I'm having trouble finding anywhere that sells replacements. Lots of companies sell CPU fans, or case cooling fans, but this is unusual. Maybe there's a more generic name for it? I could replace the whole motherboard (I've had this one for at least 5 years), but then I'd also have to replace the RAM; I'll have to do that eventually, but for now I'd prefer a cheap solution, since I'm sure this component only costs about £5.
Any suggestions from the HiveMind? (For reference, this mobo is an MSI 875P Neo.)
Edit: Apparently this is called an "NB fan" (NB = NorthBridge chipset). I'm off to the Tottenham Court Road computer fair, so hopefully I can find a replacement there.