Hey there,
The only moving parts in the Wii U are going to be your Disk Drive or the Cooling Fan, and since it doesn't sound like your console is having issues playing games, then it's a cooling fan issue.
My advice if you're cool with it, would be to open the console up and try to get at the Fan. Make sure that it is clean, and is spinning freely in its housing. I'd also suggest that you replace the current Thermal Paste with some fresh Thermal Paste.
I get that this question is a few years old, but hopefully if someone else is having this issue, then this can help them.
Best of luck to you!
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I also have a constant buzzing/vibrating noise - but other than that the console seems perfecty fine. Interested to know the cause of this as I bought the console this way second hand.
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