I don't have that exact problem, but I do have a 60GB PS3 with some major issues. I bought it used, and it worked perfectly for several years. When God of War 3 came out, my PS3 had some issues with it. After running it for a few hours one night, my PS3 overheated and shut down. From that point on, any graphically taxing game makes the PS3 shut off after about 30 min. And the problem slowly gets worse, so that less advanced games now have the same issue. There are certain games like Star Wars TFU that have specific areas that make the PS3 shut down instantly, apparently due to the large number of data being processed or something.
I took it to a local game repair shop and they tried a few things with it before determining that the motherboard was shot. The only solution is to buy a new 60GB PS3 motherboard and swap them out. I'll probably just shell out for a new slimline PS3 eventually, but I'd hate to lose the backward compatibility.
One thing that pisses me off though is that the repair guy told me that one of the updates put out by Sony last year makes the fan run more slowly on older PS3s, so that they die off and the owners need to buy new ones. If that's true, it's a crock of shit.