I had the same problem with my time capsule (A1470). The fan would kick into high gear several times a day and then eventually it began to squeak and then the fan died. I took the Airport apart and left if running with out the case in case that would be cool enough. Look at iFixit for a rough guide on taking it apart.
Eventually my Time Capsule would overheat and reboot.
So I removed the fan and googled for a replacement. The only ones I could find were in China and would take a month to arrive. That wouldn't do, so I googled on repairing this kind of fan, but all that I could find said that you can't repair them. Well, I figured I had nothing to lose, so I opened up the fan and applied a little oil on the spindle of the fan and put it back together. First I tried WD-40, but that only worked for a few minutes. Then I used some oil that I had lying around that came with an electric shaver.
I've been running it for 24 hours and so far so good. It's still doesn't have the case and I can see that the fan runs continuously at a low speed. It hasn't kicked into high speed mode and it hasn't sent any warnings about overheating to the Airport Utility running on my desktop.
I cautiously optimistic that it has been fixed.