Sorry, maybe my taxonomy is different. I mean a full-scale war, not whatever those were. A war with roughly equivalent militaries and economies, where there is a threat and war footing that might justify changing the lives of civilians and their relationship to their government. Technically, Congress hasn't declared war since 1942, even though we've been in some big ones since then, but that's not what I mean either. We probably need a broader vocabulary to describe the various uses of force in international relations, which distinguishes between war and military actions, however expensive.
I think any context in which the US invades another country and kills a million civilians is a “hot war.” Otherwise, you’ve gone so far down a “war is peace” rabbit hole that you’re no longer in touch with reality.
Afghanistan? The Iraq War? The people we drone strike every day?