i would say you need to turn it on and look in the back. i would bet your fan is not working. its a easy fix to do your self i have repaired lots with this issue . you may be able to stick a toothpick in there and bump the fan to get it working again. but i would replace it as it is going bad ;)
Sounds like overheating, but when game does not work in like 30 minutes, it may be two things.
1) Game disk if you play games what you get from game stores OR Flash memory if you play downloaded virtual console/wiiware games.[
2) Do you have problems with other games? If not, it can be the optical drive.
If you have warranty left, take it to nintendo to be repaired.
If you don't have warranty, here is a link to an new wii dvd drive:
Replacement disc drive for the Nintendo Wii — 4 available at 79.95 each.