I have the same problem. My PS3 is the fat model too, but the videogame turns off not only in an specific part. I tryed to move it to a place with better refrigeration (even its actual place having enough space for air circulation and great conditions of working), I changed its orientation to vertical, and the problem persists!
I have the same problem with my Fat PS3 too. I read from forums that a lot of people are affected by the same problem. The PS3 would just shut down with 3 quick beeps and blinking red lights. Some mentioned that The Last of Us squeezes every bit of the PS3 resource and causes the system to overheat. In any case, I believe any game developer should fully test their games with all the console SKUs, including the old ones. It is unacceptable that the game runs on the newer systems but not on the older ones. I hope that Naughty Dog hear our plight and release a patch or something to rectify the issue. I've stopped playing The Last of Us and the issue occurs too frequently. Thanks.
I called to the phone number of the technical assistence indicated on the TLoU's manual (sony technical assistence), and the guy said to me, that the problems of the PS3 software version 4.45, weren't totaly solved on the 4.46 (that would be causing the defect), but sony was working to release the 4.47 this week. Until now, nothing!