Why is my computer crashing?

That's not a lot of information to go by, but i would look at your temps while playing Skyrim, even if your BIOS is reporting 60c then i think it would still be best to check in game as your BIOS is giving you a reading without much/any load so during gameplay i recommend seeing how high it gets before shutting off. Also check GPU temps as well.

Also try other resource intensive games if you have any, BF3, Crysis etc and see if the same thing is happening with those games, as if it is only just happening in Skyrim then it's a different issue altogether and i'd probably recommend installing new drivers in that case as my first troubleshooting effort.

How would one check temperatures from anywhere besides the bios? This is my first build, so I wouldn't know if its software I need to download or something that sould already be on the computer to check the temperatures.

Download hardwaremonitor, its a useful and (usually) reliable one thats free
Moto

Could you provide a link please, because when i googled that i found a lot of things that were not free and could not tell what you were referring to exactly.

http://www.cpuid.com/softwares/hwmonitor.html
sorry for delay on answer man,  
Moto

No problem whatsoever.

Crack open your computer case and look at the CPU fan.
Is it running?
Is it full of dust?

If its not running, replace it.
If its dusty, vacumn it out, or blow it out....

Getting a "utility" to tell you something that you already stated(its running hot, 60 degrees Celsius) doesn't solve the problem.

Its only a few days old and I just downloaded the drivers, so either something is defective or the stock heatsink isn't sufficient for Skyrim.

I plan to get the Corsair H40 to cool my CPU.

Also, how much can airflow in the case affect the CPU temperatures?

Not much, most CPU heatsinks have there own fan/s that move enough air to the point where adding case fans will only at most generally result in a 1c-2c drop in CPU temperature if they're placed properly, case fans make little difference in CPU temps, they're really only a factor for components that need to be passively cooled.

Check to make sure the heatsink isnt loose.

Also, a little bit of wiggle in the heatsink is normal, if its able to move more than about an 1/8 of an inch, it may not be seated correctly.

Best answer selected by Acolyte_64.