I had a similar problem a few years back with Brawl. It is a dual-layer disc, so data is piled on in layers on the disc, and so somehow that means it overheats the Wii more easily.
I was playing Smash Bros Brawl for a very extended period of time (probably 7 or 8 hours) and then i turned my Wii off, and the next day, it wouldn't read any discs. But VC and WW would work fine.
Apparently others were having similar problem, because on Nintendo's support website they had a troubleshooting section just for Brawl, and my problem was listed in that section. Nintendo was offering to repair the Wii for no cost, so I sent it to them, and they sent it back in a week or two, and it was all fixed. Haven't had any permanent problems since. I don't know if it is too late to get it repaired for free, as the game is 4 years old, but they would most likely repair it if you paid for the repair. You would need to make a repair order at the customer support website, and they would give you instructions of what to do.
if I were you, I wouldn't trust myself taking my Wii apart. It turned out badly when I tried to repair my DS. But if you think you can do it, then you might as well try.
If anything goes wrong, or if you choose not to repair it, I would wait for the Wii U.
Been away for a bit, but sneaking back in.
Gaming on: PS4, PC, 3DS. Got a Switch! Mainly to play Smash
