Though Nintendo UK denies that it has received any reports of Wiis being bricked due to the WiiConnect24 service, you can never be too safe with any $200+ investment. Xtremetuner has created a hardware mod with the specific intention of guarding the console from overheating while it is in standby mode.
WiiControl acts as an external interface that monitors and displays the temperature of the system on its LCD screen. When the mod detects temperatures beyond 35°C, it automatically activates the Wii's fan, even in standby mode. An audio warning will also notify the user if the temperature ever exceeds 44°C. The fan is disabled once the console has cooled down to 30°C. Check past the post break for a video demonstration.
See also: Temperature-monitoring case mod for the Wii