Fat32 is just your file system, NTFS (New Technologt Filing System) is the newer file system. Among other thing,s it allows you to make better use of your hard drive space, as it allows you to store more information on the same size drive\partition as a Fat32 same size filing system can.
NTFS is also a lot more security concious and capable. It has not however got anything to do with your computer shutting down.
Some initial straight forward things to help the shutting down problem to try are,
Run windows update, and any virus program that you may have installed.
As Gman says, overheating is a common\the most common problem for a PC shutting down. Buy a can of compressed air, take the normaly left hand side cover of your PC off (asssuming it is not a laptop), and blow all dust from motherboard, and especially CPU fan and cooling vents.
Again, as Gman stated, switch comp on while side cover is off and make sure fans are working.
Remove all sticks of memory, blow the slots out with compressed air and replace (computers hate dust bunnies).
Make sure you have all blank card slot covers REPLACED from any PCI cards that you may have removed (this allows air circulation to stay inside your system, cooling the motherboard\components and not escape from said gaps).
Check device manager and make sure there are no conflicts (especially with graphics). Device manager needs to be rosy in the garden with no Yellow warning signs etc.
Download the free program malwarebytes and run a scan.