Over heating would be a sign of a computer shutting down unexpectedly. So will a failing power supply.

The overheating is usually associated with extreme computing such as gaming...do you remember what you were doing during the shut downs?

Your friend is correct about moving the compuer from the carpeting...it will gather more dust there than anywhere else....just simply raising it up and sliding a board or some solid hard surface material that extends about 4 inches all around will reduce the dust build up by 40%. The simplest way to determine if you are experiencing heating issues is to open the side cover and expose the motherboard to the open room and point a house fan to blow cool air inside....if no more shut downs then it is a good option that overheating is the problem.
Fans are noisey to begin with....sometimes if the bearing get dry they become even more so. Most of the noise is not caused so much as by the air flow but by the restriction of the air flow....so make sure all the screens are cleaned...Another thing with noise is vibration noise set up from the fans,,,this may sound like a hum more than anything else but can cause the metal brackets to vibrate and rattle inside and also the wires to vibrate and rattle or slap the framework inside the computer...moving the computer could have jolted the wiring and stopped the vibrations and now make the fans much quieter than before.

Quiet is good....lol...so long as the fans are still working.