Macbook Pro (Retina, 15-inch, Late 2013) keeps turning off on its own

Hi guys. I have a little problem with my macbook. It keeps turning off on its own. This started happening about 2 months ago. The screen first gets black, but it's still turned on, then the fans start blowing, and after some 15 seconds it turns off. After I turn the macbook on again, all the windows open up again as if nothing had happened. If I turn off the computer while the fans are still blowing, a little window shows up that tells me that the computer was unexpectedly shut down (however, this always happens if you simply turn off your computer). Also, when the macbook is in "Rest mode", the fans start blowing wildly, and they'll never stop until I press the shut down button for a while.
I tried running the hardware test (nothing seemed to be wrong), I reinstalled iOS like 3 times (also tried resetting to Mavericks), but nothing changed. Then I partitioned the hard disk and installed Ubuntu there. On Ubuntu, the macbook only shuts down when in "Rest mode". Otherwise everything runs perfectly fine on Ubuntu (the computer just runs a little bit hotter than usual).
Then I realized, while talking to a friend on iOS, that the computer doesn't shut down when I'm talking on skype. Therefore I got myself a second account on skype and talk to myself whenever my computer is turned on. Everything runs perfectly now.
Does anyone have an idea what could cause this weird problem?

Best regards, Patrick