I am digital only and it is almost silent,but with physical it will be a bit louder but nothing you will notice,my PS4 is much louder even with digital games and gets really hot while X1 is cool and quiet and don't expect X1 to have the problems the 360 had,my 360 slim model is much louder then my X1 if you want to use that as an example.
Disc should only spin during install and startup, so that shouldn't be an issue. No idea how your XB1 stays that cool, mine is like a heater. It is in a pretty confined area though. --- https://www.youtube.com/user/Bandin6385/