My Wiiconnect24 is actually fairly active! I get probably 2 messages a day (maybe), and I use most of the channels that work better using WiiConnect24. Once Animal Crossing for the Wii comes out, I think (and this is not comfirmed) you can use WiiConnect24 to allow your friends into your town even when the game is off! Of course, you can turn this off if you don't like people snooping around in your town while you arent looking.
Also, WiiConnect24 does not cause overheating. When the console is turned off the hardware inside is barely active, and Nintendo designed the Wii to withstand the heat that the Wii generates when turned on, so really there isn't really harm done. If you really think that WiiConnect can overheat your Wii, then you could get an extra cooling system at any store that holds video game hardware.