My four-year-old MacBook has started shutting itself down

Question

My four year and one month old white Macbook, running Snow Leopard, has started shutting itself down - as in suddenly going from being on to being in a powered-down state - in the last two days.  In the last two days, it has shut itself down at least six times, I've lost count.  Before the last two days, it never shut itself down ever in four years that I can remember.  Five out of the six times it shut itself down, I was playing a PlayStation game via the PCSX emulator for OS X.  I had been playing this game on and off for about a week, give or take a day, before this started, without issue. 
Yesterday, I started playing it, and the macbook shut itself down some time into it.  Thinking it was an overheating problem, I let it cool down for 15-20 minutes and tried again, and the macbook shut down again after maybe 10-15 minutes of use.  Again, I let the macbook cool down for 15-20 minutes, the results were the same.  I went through this again, this time ejecting the DVD that was in the drive and unplugging the power cord(to let the macbook run on battery, to see if that would make a difference), and it shut down again.  I then let the macbook cool down for probably 4 hours.  I then engaged in a two hour internet surfing session, in which the macbook did NOT shutdown.  I turned the computer off when I was finished, and a few hours later I tried the game again, and the macbook shut down again, after only 5-10(I think) minutes of use.
This morning, I tried again and there were was another shutdown.  After this, I tried another game(with another emulator), a 2D one as opposed to the 3D one I had been trying, and this went off without a hitch.  After that, I tried a different 3D game(in yet another emulator), and the macbook shut down again(and in this game I hadn't even started anything yet, I was just at the first menu screen were you select a save slot, that kind of thing).  After that, the computer was off for the rest of the day until the last two hours, during which I have been online, and there has been no shutdown as of yet. 
I know this is a lot of detail, but I just wanted to illustrate the possible correlation between certain games and the shutdowns, even though I emphasize that I have played all of these games before without issue.  Additionally, I watched a full two and a half hour movie via DVD on my macbook either the night before or two nights before the shutdowns started(having trouble remembering) without any issue.  If it's an overheating issue, it just seems strange to me that it would get through a two and a half hour DVD without shutting down, but a game with 3D graphics - and this is mid-90s polygon early 3D graphics, not 2011 movie-like 3D graphics - would suddenly start making it shut down.
Anyway, I'm very concerned, and looking for any advice any of you can give.  Any assistance is appreciated.

Answer 1

I had two more shutdowns occur.  The first was while playing the same game that cause most of the previous shutdowns.  I had Activity Monitor open, and the CPU % was way over 100.  The second was while playing a 2D game, marking the first shutdown during a 2D game.  The CPU % wasn't as hight as the first time, but still up to around 75-85 or 90%.  I didn't notice the fans ramp up, but I may not have been listening hard enough.