One possibility is that the computer could use a little cleaning out. Over a two year period of time a lot of dust can accumulate inside the laptop, if you have pets this increases the accumulation.
As for the battery, what you are describing sounds like it's dying, a low battery level shouldn't cause the kind of heat issues your describing.
If you would like to monitor your temps without entering the BIOS, download Everest Home Edition, it's freeware, and makes it easy to check temps and other aspects while still being able to operate the computer.
http://www.lavalys.hu/products/overview.php?pid=1〈=en
dcc
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It must be getting late, I just now noticed that you wrote that the temps where between 65 and 70 degrees celcius...that's between 149 and 158 degrees F., yeah I'd say that would be shutting down you computer. While you have it open, check the seating of the CPU, and the heat sink. Does the heatsink have a fan, if it does, is it working.
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