Ubuntu 18.04 LTS Random Shutdown with Nvidia RTX 2080

I have a brand new laptop with a Nvidia RTX 2080 and I am facing brutal stops at random. I've already reinstalled the driver several times (now via ppa, as mentioned here: How to install Nvidia drivers?

In addition, I checked the temperature of the processor (I9 9900K) with the sensors and the temperature of the GPU with nvidia-smi -q -d temperature as shown here: How to see the temperature of the video card (Nvidia, ATI , Intel …)

I've also checked if new is enabled as shown here: https://docs.nvidia.com/cuda/cuda-installation-linux-guide/index.html#ixzz4rQODN0jy (scroll down to section relative again)

Secure boot is disabled. I have an M.2 card with Win10 and an SSD with Ubuntu on it. The problem seems to appear when I restart out of Windows, then I launch Ubuntu (by pressing f7 to access the boot menu, etc.). It also happens once on a new startup.

So, when the sudden and random shutdown of Ubuntu occurs, the computer then turns back on and I can press f7 to start Ubuntu. I'm not really sure, but it never happens if I start Ubuntu and restart it again. I've already checked the logs / var / log / syslog kern.log etc. but nothing there. I am not a Linux pro, so I do not know where I can find information on such "accidents". Any help is appreciated.

EDIT: This problem did not occur in Windows 10.