As the Wii is rather simple compared to the other consoles, more like a slimmed down but upgraded GameCube I think overheating problems should be very few.
Minus overheating issues I think most likely moving parts are going to fail in a console, so the disc drive for the Wii as the console doesn't have a harddrive (and fans can be much simpler). Compared to the PS3 (Blu-Ray being new and more advanced tech) and XBox 360 (discs spinning like crazy, resulting in quicker wearing and potential disc scratching) I think the Wii is still likely less prone to such issues as well.