When this has happened to me and to family members, (and it's happened a few times) it's shut itself down due to overheating of the CPU. Improper use of thermal grease between the CPU and the CPU fan would be one guess; a misaligned CPU fan (where it's not securely fastened evenly to the CPU) would by my other. Either way, the fix is the same. Replace the thermal grease.
First, purchase fresh thermal grease (there are many brands, do a bit of research to find the kind you want or need.) Thermal grease is cheap, and a tiny tube will last a long time. It's cheap insurance.
Next, take the CPU fan off the CPU, and as you do, take note of how the fan is mounted and how the fan mounting hardware works. Also check to see if the fan is wobbly before you unscrew anything, that's a strong clue you're on the right track.
Look at the existing grease that is on the CPU and bottom of the fan's heat sink. If it's crusty and hard, or gobbed on any thicker than a sheet of tracing paper, that's also a strong clue that you're on the right track. The adhesive stick-on grease pads that fan makers used to use are horrible conductors of heat, and if you find one that might be the problem.
Clean off the exposed surface of the CPU chip and of the bottom of the fan's heat sink. I use dry paper towels to first mechanically remove as much old grease as possible, and then clean both surfaces with a paper towel lightly dampened with 70% isopropyl alcohol. Clean them to a bright finish, don't allow any old thermal paste to remain, and don't dump the liquid alcohol directly on the CPU. (If you still get the motherboard damp anyway, a blow dryer set to a cool setting for a few minutes will evaporate what's left. Be careful not to start a fire, alcohol is extremely flammable and many things on the motherboard will burn!)
Clean any dust and dirt from the heat sink fins and from the heat sink fan. Compressed air is good, a old toothbrush works, pipe cleaners, anything to get it clean.
The surface of the CPU is very flat silicon and won't need attention, but make sure nothing is sticking up above the top of it. The surface of the heat sink also needs to be flat, but because it's soft aluminum or copper it might be gouged or dinged through rough handling. Make sure it's undamaged. Be careful if you think you can use sandpaper or other abrasives to correct some damage, as it's very difficult to get the surface as flat as it needs to be without proper knowledge and tools.
(If the metal surface of the heat sink is damaged or the mounting connectors or hardware are damaged, strongly consider buying a new CPU cooler. Be sure to buy one rated to dissipate the amount of power your CPU draws - an 80W CPU chip needs a cooler rated to dissipate at least 80W.)
Apply a very thin and even coat of thermal grease to the CPU chip. There are really good online videos on how to properly apply thermal grease. A good coat is so thin as to be almost see-through.
Remount the heat sink and fan. When mounting the heat sink, be sure each of the four corners is equally tightened by the connectors. A stripped screw, broken plastic expander, damaged socket, bent piece of metal, anything like that can prevent even pressure from being equally applied to each of the corners. If the pressure is uneven, there will be less contact between the CPU and heat sink on that side, and that gap will cause the CPU to overheat. A proper mounting will feel solid.
Once it's back on, and secured so there is no wobble at all, be sure to reconnect the fan's power supply wire (they're often connected to a pin header marked CPU_FAN on the motherboard.)
Good luck!
