The Cold War was so named because the guns were cold, i.e. not firing and therefore not hot to the touch. Yes, there were proxy wars between client states in which both superpowers were deeply involved, but they never took direct military action against one another, a most unusual situation historically and one deserving this distinctive name.
Therefore, please do not use the term as if it meant a chill in international diplomacy, talking about the war being especially cold when diplomatic relations were particularly frosty, or about it "warming up" or "thawing" on the arrival of détente. That's not what it means. Thank you.