Relative to the Cold War, where biggest threat was the paranoid Soviet leadership overreacting to their expectation of a first strike by the West, there don't seem to be that many scenarios where a war seems likely.
I also wouldn't say a scenario like that has become less likely, depending on how you look at it, especially in the context of US nuclear force modernization [0], it could actually become much more likely.
Because irrational people exist everywhere and I have no doubt there are plenty of people around, some of them probably in very powerful positions, who are still busy "wargaming" a thermonuclear scenario in which they could end up as "winners".
[0] https://thebulletin.org/2017/03/how-us-nuclear-force-moderni...
As for the war threat - both sides had their hotheads during the Cold War, but in the end they were overruled.