I was free to do some survey for you.
Not sure if it helps but it is related.

P/s But after reading the error and the solution over the net is just by changing the country in wii settings.

Country Setting

Those that have tried to set the country to Singapore would already have noticed that you are unable to enable WiiConnect24 after that; specifically "WiiConnect24 and Wii Shop Channel service is not currently being offered". I believe the issue here is more related to legal or release control than technical, since the Wii hasn't officially been launched in Singapore. Setting it to another country works better for now.
Note that changing the country setting requires a reconfiguration of Parental Controls and WiiConnect24.

recommended setting: United States (able to review and agree on user agreement for WiiConnect24)

http://forums.gameaxis.com/showthread.php?t=1476750

---

Added on December 19, 2009, 3:06 amAlso maybe read up ere too
http://www.nintendo.com/consumer/systems/w...onnect24Problem

http://www.nintendo.com/consumer/systems/w...erAgreement.jsp

This post has been edited by paige.pc: Dec 19 2009, 03:13 AM

You can go to Wiiconnect24
Turn it on
Go to Standby turn it off. (for wiiconnect24)
So that when you on ur wii to play , the wiiconnect24 eventually turned on (as you dont need to go in and out of the settings to on or off it)
And when you put in standby mode ur WII , the wiiconnect24 eventually will off itself.
So that this will prevent from heating.

If your wireless router and your wii is too far away from each other between walls and etc.... the signal for Wii to receive is lesser.

You should be able to fix this simply by changing your Wii from whatever country your in to a different one.

1. Access the Wii System Settings (how to).
2. Click on the blue arrow twice to reach the Wii System Settings 3 menu options.
3. Select "Country" and press the A Button.
4. Use the scroll bar to find the country you want and select it.
5. Move the cursor over "Confirm" and press the A Button.

You should be able to fix that problem just by saying you live somewhere else.

Another solution
re-make your network connections, this will solve it.

Another solution
EDIT: ok scratch that i had to change the router channel from 11 to 1 to get it to work, cheers anway... even though nobody viewed this problem

Another solution
here was a problem registering the console to the WiiConnect24 service. What to do:

* If you have multiple routers and/or modems, try to connect to no more than one router and one modem try connecting from another location.

* If you are using only one modem or router, something on your network or from your Internet Service Provider is blocking the connection. You may need to contact your service provider for more information.

* If you do not have the ability to connect from another location (such as a friend's house), please call 1-800-255-3700 so that we may discuss available options.

Another solution

Wii Error Code 51300 - 51399

This error is caused by the Wii being unable to connect to the access point.

To solve this error :

Try changing the channel of your wireless router to either channel 1 or channel 11 which can increase download speeds.

If your router is using WEP encryption

* Ensure your key is hexadecimal, consisting of 0-9 or A-F only, no other special characters or letters.
* 64 bit encryption requires your WEP key to be 10 characters consisting of numbers or leters A through F.
* 128 bit encryption requires your WEP key to be 26 characters consisting of numbers or leters A through F.

If your router is using WPA encryption, the Wii is compatible with :

* WPA - PSK(TKIP)
* WPA - PSK(AES)
* WPA2 - PSK(AES)

If your router is using MAC filtering, ensure the Wii MAC address has been added to the list of approved MAC address on your wireless router settings

This post has been edited by paige.pc: Dec 19 2009, 04:13 PM

WC24 in there the settings theres a standby mode option press it OFF.
And then you are done.
So when ur wii is on standby mode , your WC24 is turned off automatically.
When you turned on ur wii , WC24 is turned on by itself.

Meaning your wii is not getting warm and warmer and heating when your wii is on RED colour on the Power button ( which is standby mode )

Yah exactly what RAMChYLD said. Are you sure it is RED the power button.
Cos my wii was set to this settings since i guessed few months ago.
I dont feel any heat to it in standby mode.
And also i dont get any updates from nintendo if my wii is on standby mode as well.
Only will get the updates when i Power On my wii ( thats when WC24 is on automactically )

As for last time before i had GH5 , normally i will just turn on WC24 from the settings if i need to use this function.

After i started playing GH5 or etc, thats when i use this function by turning the WC24 standby mode OFF.
Cos for convienient sake , i dont need to go to settings on and off each time that is becos GH5 online uses WC24.

Hmmm.. i wonder urs is different?