|At a guess I think it is probably the CPU cooling fan and heatsink which is clogged up causing your CPU to heat up and eventually the laptop is shutting down due to its CPU thermal protection feature.|
Blowing hard into the fan exhaust vent can sometimes clear it and makes the CPU run cooler. Alternativly a jet of air blast may also work.
Better still if you are confident and able to do so, you could open the laptop and clean up the fan heatsink assembly.
☺ When everything else fails, read the instructions.