Well, if you've purchased the warranty like you said you have, then you may aswell take it back to the store. If you're lucky they might give you a new one on the spot, or at worst it may take a couple of weeks. I have no idea of the supply and demand over there, but in Aus you can just walk in and get one.
This hasn't happened to me when I play Wii Sports Baseball or any other games, so I dunno.
Just see what they say.