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 "/Users/mac/Library/Logs/Skype". 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