Do I need external hard drive for wii?

So I play zombies on COD black ops, but every time we get anywhere passed level 20 either the wii freezes or people including myself get disconnected. I keep the wii in a openly ventilated and try to keep the area cool so it doesn't overheat (kinda lame that I have to baby the console). I have seen people say that the wii hardly has the capability for zombies. So is this true do I need to go purchase something just so I can complete a game?

Any info on why zombies always craps out one way or another would be appreciated. Thanks