This is copied from a reply I posted just a couple days ago in another thread, but I suspect it is your problem, too.
If this fan is a few years old, what you describe sounds like worn bearings. Typical symptom pattern of that is:
1. Fan starts to make odd noise when it first starts up after being off for a long time. Noise lasts a short time, then stops. If you reboot there is no noise. But if you shut down for a long time so everything cools off, the noise is there again for a short time after boot.
2. As time goes on (over a few months), the initial noise lasts for longer and longer, but does stop eventually.
3. At some point the noise is always there.
4. In the end, the fan seizes up altogether and makes NO noise because it does not turn at all.
If that's the pattern you see developing but it still does not make noise all the time, then this is the time to replace the fan. There is no way to repair it, and you can NOT add oil to fix it. Be sure to replace BEFORE it seizes up so you have no cooling from it.
This may apply to either or both of the CPU cooler fan and the case's only general ventilation fan. If either is badly worn and noisy, that also means it is turning too slowly and NOT providing good air flow to cool.