She was 'burning for' a chance to prove herself. [=she wanted very much to get a chance to prove herself]
('humorous') “We were talking about you last night.” “That explains why I 'felt my ears burning'.”
She was 'burning with' anger at his rudeness. [=she was very angry because of his rudeness]
(..) The witch - she can bring baby. I hear her say so. Are you in agony, my lion? - No. - You look like you're in agony. The fire is burning your pretty soft skin. - Ah! Damn you, woman. Are you immune to pain? - Just used to it. - Drink. (..)2011 TvShow: Game of Thrones Title: Baelor Season: 1 Episode 9