I've had two problems with noise with the old Wii
1) Dust. It was sat idle for about three months and after that started making awful noises when there was a disc in the drive. The careful application of a vacuum to the disc slot and air intake on the bottom and fan area took care of that.
2) Balance. new TV cabinet wouldnt take Wii vertical so off its stand it came (seemed to make even less noise after this as well). But then I started playing Metroid Prime, everything seemed fine till I popped in a Wii game and I started getting odd noises, long load times and stuttering music.
I'd lazily opened the flaps for the gc memory and controller but not removed them so the Wii was on a very slight angle, removing the gc stuff and closing the flaps stopped the problem.(I know I could have removed them)