It would have 'melted your heart' [=it would have filled you with compassion, sympathy, etc.] to see her lying in that hospital bed.
Her anger 'melted away' when she saw that he was truly sorry.
He seemed to 'melt into' thin air. [=he seemed to disappear]
(..) out is how she survived. I put a bullet in her myself. She shattered into a thousand pieces of ice. Ice melts. I'm gonna take a wild guess... That your being here isn't a coincidence. I'm here... (..)2009 TvShow: Heroes Title: Chapter One 'Orientation/Jump, Push, Fall' Season: 4 Episode 1