another thing to add, if you have viruses, spyware, etc. etc. on your computer and you backed the os with all your programs and files, then you restored them one day you still have all that viruses and spyware, you dont get a clean start.
you wouldnt want to store your operating system on a extrnal drive. You would just store your files that you want copies of. if you did the os with all your files in programs, you would have massive backups.
the intake is probally just full of dust so its harder for air to get into the case so the fan has to work harder to move the same amout of air. If you clean the inside of the front of the case it should work much better.