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.
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.