The PS3 is apparently overheating while playing L.A. Noire because of firmware. That's according to a retracted statement from Rockstar, the studio behind L.A. Noire, adding that the issue persists mostly with older PS3 consoles. But the PS3 isn't alone.
There are reports online that the Xbox 360 version of the game is locking up. "It's been freezing since the first mission, now I'm about 4 in and it won't stop freezing," wrote one player on the Xbox.com forums.
Rockstar seems to be aware of Xbox 360 issues. Part of the studio's advice is to "clear the 360 cache" (read Rockstar support here).
Many players are not experiencing any issues whatsoever. But those who are, try clearing the cache. If that doesn't work, there's always bitching on the internet.
Freezing!! - L.A. Noire - Forum [Xbox.com]