I don't know if this is your problem but you should keep this in mind until you solve it.
I saw something similar with a cheaper and older laptop once where the owner came to me for help. He then proceeded to show me how he could make it restart by holding it by the edges and bending it ever so slightly.
"AAAAHHHHH Stop that!" I yelled.
His problem was that as the interior of his laptop would heat up after starting and it would expand something inside that apparently caused a solder or cracked trace connection to microscopically disconnect and then reconnect. His died after running a few minutes, rebooted and then ran fine until he turned it off and let it cool down (or bent it LOL). He stopped traveling with it and it lasted him at least a year until he got something newer and then gave the bad one to a relative.
Anyway, the electronics in XPS16 are some of the most complex electronics available on the consumer market. If it is under warranty, I would pull the harddrive and send back the laptop for a repair or replacement. If it isn't under warranty, I would be careful not to bend it even slightly (like you can bend it at all
but you know what I mean) and I would do regular backups of important data.
It could definitely be something else. I just thought you should here my story.