"I'm a cold guy but I'll eventually grow to love you."

Okay, so maybe the guy isn't always a so-called 'cold city guy', but variations of it are rampant - the arranged marriage ones are usually spin-offs of this as well. The term for this is tsundere (according to wiki, it's a 'Japanese character development process that describes a person who is initially cold and even hostile towards another person before gradually showing his or her warm side over time'). Common storyline: girl likes guy but guy is emotionally detached from the world/just an emotionless (or very hostile) idiot who eventually falls for the girl's warm and lovely personality.

Heart-warming transformation? Probably. Overused? Definitely.