Andrei Piontkovskiy, in addition to two known World Wars, considers the Cold War as the World War III and the current war in Eastern Europe as the World War IV. His parallels are that WWII was fought by Germany dissatisfied by the results of WWI, and WWIV is fought by Russia dissatisfied by the results of WWIII.
World wars involve many countries, and Cold War definitely qualify. Today's war is a pretty active, quite large "hot" war, which also involves many countries - even though most fight by proxy.
I also think "Cold War II" for the current situation is more fitting.
I think if there is any useful distinction between "hot" and "cold" world wars then it's most likely whether super powers are in direct military conflict with each other or whether military confrontation is "only" through proxy wars.
Note that the original cold war wasn't very "cold" for much of the world either - the only thing that didn't happen was direct millitary confrontation between the US and USSR. Nevertheless there were lots of local conflicts and proxy wars where each bloc was backing a faction.
In the today's war in Ukraine one country - Russia - fights directly, not from proxies, and the other side - mostly USA, but also other Western countries - supply weapons, volunteers, intelligence services, training. It is comparable with Vietnam war, right, but not already with Afghan war of 1980-s, or small conflicts around the world. The scale of war is also quite large, the level of directly fighting forces is much more comparable.
Should we admit that world wars don't need to involve superpowers - or at least only superpowers? The term wasn't that much applicable before end of WWII.
So here we can argue that in WWIV a non-superpower fights - Ukraine, on its territory, a superpower - USA, merely - but with principal results - supporting Ukraine, and the rest of the West. We may not call it a proxy war - I agree, it's a rather poor comparison - but for WWIV term it is another matter.
World wars don't need to involve superpowers, but they need to involve large part of the world. Russian invasion on Ukraine doesn't, and it's unlikely to escalate - Russia can't, because they have neither people, hardware, or allies, and the defending countries don't have a reason to.
