The fan was making noise and I was afraid the overheating would damage the computer
It went well by and large. There were a few problems. I was not able to remove the old fan without tearing the black felt tape, in fact I ruined it in the process. I worked around this by replacing the pieces as well as I could and then securing the whole strip with paper tape (the kind you use for first aid).
Also, when I inserted the left screw to install the new fan, the screw would not seat into its threads. I had to remove the new fan again in order to figure out what was wrong and I found that the plastic housing for the threads of that screw was all cracked and when I tapped it with the spudger, it fell apart. The pieces and the brass threads for the screw scattered into the computer. I was able to get all the pieces out and the brass threads so I just ignored the fact that I could not use that screw to secure the fan. I had to assume that the right screw and the one passing through the other hole (coming from the outside) would be enough to secure the fan. So far, so good.
Warn people about the possibility of losing one or both screw housings on older models (mine is Late- 2006). I presume this problem occurred because of dust build-up on the left side of the fan at the heat sink causing unsymmetrical overheating on the left side of the fan compartment. This overheating could be the cause of the plastic degradation.
If possible, find a way to fix the screw problem and the tearing of the black felt tape. I noticed that you don't sell the tape so there seems to be no way to replace it.