Hey and welcome to WiiChat.
I experienced a similar, although not quite as severe of a problem. When I completed my first update, it took me about an hour to complete the update, at first I thought my Wii froze, but everything will still responsive (ie. Wiimote cursor still moved around, etc.). If at all possible, just leave your Wii on until you wake up tomorrow morning if it's not possible for you to wait. I don't think you'll need to worry about it overheating since when the Wii is in the ON status, the fans are on and help cool the system down.