We're going to need more information on the computer if you're looking to troubleshoot... such as which CPU and OS you are using, power supply model, and which drivers you are using while the computer crashes etc. Also make sure to list any recent changes to the computer if any, including OS updates and/or game patches.
The CPU, if it overheats, will shut itself down to prevent damage. Might want to check your temps...
Also, are you using Radeon Settings to control the cooling fans and/or power limit? The 390 series is known to like to use a lot of power and if it's starved you could run into some issues with crashing. Regardless, the first thing I would try is to do a complete uninstall of the graphics drivers through windows and then boot into safe mode and run Display Driver Uninstaller to purge any residual files.
After that's done, reboot the machine and download and install the latest AMD drivers for the card and OS. Select a clean installation when the setup starts and if the setup prompts another reboot, do it. Once you've done that, right click the desktop and open Radeon Settings. Check the global settings and raise the power limit up to +10% and apply and save the settings.
Test the game again.