Having DX11 crashes as well using an i5-6400 and R9 380 4GB.
Other games that use DX11 have no problems at all, the card remains cool during playing as well and the crashes seem to appear at random. Sometimes the game crashes after 5 minutes, the other time after 2 hours. I have tried to rollback my drivers to an older version to see if that resolves the issue but unfortunately it does not...
This is quite a shame as I literally bought the game yesterday after playing the trial on my laptop which had no issues with the DX11 version at all.