How do I know my mac turns off because of overheating? My Macbook Pro (Yosemite)  early 2011 sometimes unexpectedly turns off when running heavy tasks on battery power. Is there a way to confirm this is because of overheating?
Here's a part of system.log from the moment of shutdown. What other logs can I read?

Feb 24 08:22:56 macs-MacBook-Pro.local Skype[281]: Failed to get
contents of directory &quot;/Users/mac/Library/Logs/Skype&quot;. The file
“Skype” couldn’t be opened because there is no such file. Feb 24
08:24:47 macs-MacBook-Pro systemstatsd[583]: assertion failed: 14C109:
systemstatsd + 4269 [A886B71F-3A31-3324-9B30-5143FDF4ECCB]: 0xb Feb 24
08:24:47 macs-MacBook-Pro com.apple.xpc.launchd[1]
(com.apple.systemstatsd[583]): Service exited with abnormal code: 1
Feb 24 08:54:10 localhost bootlog[0]: BOOT_TIME 1424764450 0
It would not do that until:

First the fans go at full speed for few minutes. You would hear that.

If that does not keep the temperature from climbing, it would cut down the CPU power. You would feel that in computer becoming sluggish (slow).

Normally the above is sufficient to prevent overheating.

If all that has failed it would not just shut down, it will try to shut down correctly.

Look in the Console for kernel[0]: Previous Shutdown Cause: ?

You could look in to Activity Monitor to see what is happening while under stress.

There is also a app called Istat that displays lots of parameters.