It's hard to say what exactly could be causing this issue, but there are a few things you can try. First, use an external and/or on-screen keyboard to see if it is pressing 'shift' that is causing the shut down, or if it's the keyboard button itself. If it's the keyboard button itself, then you may want to consider replacing the keyboard.
The most likely cause of a heating issue is a fault in your cooling system. Your laptop is cooled primarily by a fan above the heat sink. Check first to see if your laptop fan is being blocked by anything. If you have your laptop on your lap or on a soft surface, it may be getting blocked.