The Airport Extreme (aka Time Machine) has developed a habit of running its fan all of the time even though it doesn't feel hot. It was not this way for the first week or so of use, Sometimes it will even over heat although its environment is not crowded or in a warm location in the room. Is this another case of an Apple product with poorly designed heat dissipation issues? Should the fan be running all of the time? Since it is in our living room, the fan noise is somewhat distracting.
iMac 27",
Mac OS X (10.6.6),
8 Gb RAM 2Tb HD 2Tb Time Machine
The fan in the Time Capsule is very quiet and is always on. It does not turn off if the Time Capsule has power.
The noise you are hearing is most likely the hard drive which spins most, but not all of the time. Since you have been adding data to the drive with backups, the drive is more active. Sorry, I don't have a ready answer for muffling the sound of the hard drive.
Actually, we have turned off Time Machine on all Macs on the network just to not have the hard drive active. As for the fan being always on and quiet, for the first 3 or 4 days the fan only ran intermittently which is why we were wondering why it is on all of the time now and although it is possible to have a conversation in the same room, the fan noise is definitely noticeable. If the fan running all of the time is normal, perhaps we will just find a location that provides adequate ventilation and cannot be heard, like in a closet. We definitely do like the Airport Extreme part of the Device.
The fan running all the time is normal, but if it's noisy, there is a problem of some sort. Perhaps a noisy motor bearing or something similar. I would recommend that you take the device to the Apple store to let them have a look.
If you did put the device in a closet (it really needs as much free air as possible) and the fan stopped due to a bad motor bearing, the device would definitely overheat and likely present a fire hazard since you would not hear the device...but might smell the smoke. If something like this happened at a time when you were not home, it could become quite serious.
I hope that you will have the device looked at as soon as possible.