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]
(..) Now she converts the last of her fat reserves into milk for her cubs. The spring sun brings warmth but also a problem for the mother. It starts to melt the sea ice. That is where she hunts for the seal she needs to feed her cubs. And she must get there before the ice breaks up. For now though (..)2006 TvShow: Planet Earth Title: From Pole to Pole Season: 1 Episode 1