I think it is rather unlikely that the US and Russia will go to war against each other. Neither nation--or, more specifically, neither nation's leaders--wants it.
For the record, neither do I.
But there was a bit of tension just yesterday, as two nuclear-capable bombers flew within 100 miles of Alaska. These were met by two American jet fighters, who escorted the bombers away: Russian bombers fly near Alaska; Air Force scrambles jets | Fox News
I will reiterate that I do not expect war between the US and Russia. (My take, for what it is worth, is that Putin is simply testing this new president, to see what he can get away with.)
Still, I think Rex Tillerson (the US Secretary of State) was correct when he recently described relations between the two countries as being at a "low point" in recent times.