The term "hot war" should, and was intended to be used, only in conjunction with the term "cold war." Meaning that a "cold war" is a non-shooting war; and a "hot war" is a shooting war. Extra examples: 1. People die in "hot wars." 2. People do not die in "cold wars." (accidents don't count).
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I assume the term Hot War is meant to be in contrast to the term Cold War. Hot wars, in relationship to the Cold War, is any type of conflict which has actual conflict resulting in violence and possible death in an open and overt arena.
The Korean & Vietnam Wars (1950-1953) & (1961-1975) respectively, were the only "proxy wars" fought during the cold war. Both of those "Limited Wars" (Limited to Conventional Weapons only-No Nukes) were "Hot" battles of the Cold War. Communist rebellions, insurrections, guerrilla activites (such as attempted by Castro's Lieutenant Che Gueverra in Central/South America), etc, never fully developed into "wars" involving showdowns such as they did in Korea & Vietnam.
Vietnam
The Seven Years War, the War of Spanish Succession and the French Revolution/Napoleonic War were the main wars in the 1700s. Below is a site I found which seems to give a decent list. http://www.zum.de/whkmla/military/18cen/18cenindex.html
No, it has not been in any wars yet. ;)