My Wii got pretty hot in WiiConnet24 mode, so I stopped leaving it in that mode and just cut it off when i wasn't using it. It runs in acceptable temps when on and the fan running, though it could stand to run a bit faster in my opinion.
DIT: I am probably going to mod it when the warranty runs out with a fan that will run faster under the same voltage, and I have several candidates lying around hat could work.