Of course the obvious problem is that if your listening at levels where a barely audible fan at 2m is distracting, then your not listening at an appropriate intensity level to make critical mix decisions. Don't get me wrong, I've been totally OCD about fans and have swapped my Axe fans about 5-10 times over, experimenting with everything under the sun, and I've built silent PC's etc. Thing is though, that even when you get the Axe dead silent (I've gone as far as to unplug it and run it without the lid for a while, monitoring the temps with a heat gun as an experiment) there is still going to be noise in the room. Even very high end studio monitor speakers have some audible noise from about 1m, there is the sound of the HVAC system in your room etc. I was actually just talking about this subject with the tech that came by to update the ANSI certification on my Acoustic Systems sound insulted test booth which we use at the audiology practice where I work.
Your simply not going to get that quiet, and more so, even if you do, based upon the frequency curves of minimum audibility, famously known as the Fletcher-Munson effect, your perception of sounds in certain frequencies, namely the highs and lows, isn't going to be as sensitive for really quiet sounds. You need a decent dB level in order to have relatively flat perception of sound. This is why sound engineers don't mix at whisper levels, you can't really judge what is going on. Its why patches you make late a night sound poor at band volume etc.
So essentially, don't worry about it, turn up the volume a little bit, and you won't hear the fan
