I just had a new (to me) failure to track down. My desktop computer started making a very, very annoying pulsing fan sound at about 1 Hz, so WHIRR-whirr-WHIRR-whirr etc. I opened the case and found it was the CPU fan, the default fan that came with a CoolerMaster 212 three years ago. Rebooted, found that it was doing the same thing in the BIOS menus, so not a fault of the operating system thermal management.
In the BIOS, the fan speed for the CPU fan wasn't showing up at all. The fan was still running - obnoxiously so, even - and the CPU temp was fine, but clearly something was wrong with either the RPM sensor or the motherboard. To my luck, I had exactly one spare 100 mm fan lying around, and using that I could determine that it was the old fan's RPM output that had failed, and not the fan header on my motherboard.
I have to say, that's not a bad failure mode: the motherboard couldn't detect the fan speed anymore, so it started pulsing the fan speed up to ensure cooling and make an audible nuisance of itself. Now I just need to order a couple more spare fans for future situations.