It sounds like it is overheating.
I would recommend you buy a can of compressed air and give short bursts through the air vents and the CPU fan which will be located underneath the laptop, once you are happy that all the dust is out of the system try running the laptop again to see if it shuts down, If it doesn't then that will have been the problem.
Please keep me posted with the results.
Good luck and thanks for using FixYa!!