This sounds like a classic symptom of the GPU overheating.
Is your Wii a launch model - or a very early one?
Have you left it in standby mode from Day1 (Connect24)?
I had the same after about 4 months, leaving the Connect24 switched on caused the wireless chipset to contribute to the GPU getting too hot. Nintendo acknowledged that it was an issue with the launch models and swapped mine out without even testing it. Symptoms started during Zelda, and then appeared all over the main menu and in VC titles as well.
If you Google "Wii GPU overheat" you'll find some images and YouTube footage of others who've experienced this.
Make sure you keep your console updated with the latest firmware version, I noticed that a few updates back my fan started periodically spinning when the console was left in standby, further proof that Nintendo knew there was an issue with the GPU getting too hot.