As pointed out, Khan was Kirk's hero. "Space Seed" need not have changed that much, and perhaps even Spock learned to appreciate the man after this episode. Khan basically embodies Kirk's own virtues of strength, manliness and fair play, merely taking them to the next level.
You'd think Kirk would know him on sight if that was the case. From the dialog, I'd say Kirk had a passing familiarity with Khan, but he was't a personal hero.