UPDATE: Rockstar has removed the support question pointing the finger at PS3's most recent firmware update. There are still references to Rockstar's theory in a separate support answer (scroll down in the comments), but it appears this accusation made some waves. Stay tuned...
Rockstar Games has received enough complaints about L.A. Noire players experiencing lock-ups on PlayStation 3 to, after internal testing, publicly respond and theorize the recent 3.61 firmware's to blame. The studio answer came in response to a question asking about a PS3 turning off while playing L.A. Noire.
According to Rockstar, there are two scenarios: the PS3 shuts down automatically or locks up, requiring the user to turn off the machine.
"We have confirmed locally that multiple games (Rockstar and non-Rockstar) overheat or freeze only when 3.61 is installed," said the company.
I've contacted Sony about the issue but Sony had not responded as of this writing.
"At this time we are recommending contacting Sony directly to report the overheating issue," continued Rockstar. "However, this is not the end of our support; we are continuing to test L.A. Noire on all firmware versions and hardware models to isolate the issues and see what can be done."
In the near-term, a patch is incoming. Rockstar cannot, however, guarantee it will solve the issue.
"We are continuing to take this overheating issue very seriously," said Rockstar.
There are some issues on Xbox 360, as well, and Rockstar has some recommendations to solve them.