It sounds like you're Wii is overheating. Turn on the Wii and reach your hand to the back of it. If you do not feel hot air being blown out of the back vent then your fan has probably died. You can probably order a fan online, but opening you're Wii would void the warranty (you have to have a special srcewdriver to open Nintendo products anyway). Try contacting Nintendo to find out if a fan replacement would be free, or if you would be required to pay for it.
Bosnoff, August 2007