Why is my laptop fan spinning loudly even when CPU is cool?

I own an HP Pavilion x360 on Windows 10, and when I powered it on this morning, the fan sounded like a jet engine. I figured it just needed to be rebooted, but when I restarted my PC, it still sounded really loud. I wondered if my core was too hot, so I checked my core temperature and it was in the 40-50 celsius range. My PC isn't being slow or anything either. Why is my fan going nuts, and what can I do about it?

Question by user40146 on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.