Asus laptop...the infamous overheat issues.

Your laptop switch off itself is because there is a BIOS setting that let the laptop goes off without actually overheated.

Open the lower part of the laptop and use blower to blow off the dust..I will use vacuum cleaner to suck the dust but it is not recommended.
Or send it to pc repair shop to let them clean it for you, apply some fresh new heat-sink compound between the heat-sink and processor.