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]
(..) and you've made three. (knocking) Hey. Where are the guys? Oh, they went to the store to get solder, which is metal you melt to make science things. Since when do you work on weekends? I'm an astrophysicist. The stars don't take a day off. (..)2016 TvShow: The Big Bang Theory Title: The Solder Excursion Diversion Season: 9 Episode 19