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]
(..) it sucked all the reactors dry. It's done feeding. What's this? Jesus, it's the same pattern. Fifteen years ago, it's what caused the melt down! It was an electro magnetic pulse. That's what it's building to... converting all that radiation until it hatches. You have to shut down. (..)2014 Godzilla