Laptop keeps shutting its self off

NOTE: If the laptop is under warranty, be sure you contact the manufacturer before doing any work at all inside it.

Just blowing into the vents won't cut it if it is over heating. It will need to be opened up and have all dust and debris removed. Should that not be enough to cool it down, then the thermal paste should be replaced. If even that doesn't do it, your fan(s) may need replacing.