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]
(..) with a marked face of lslam. He carries a Saracen sword. I'm sure it would take an army to match these rogues. I trust Locksley visited his manor and found the home fires still burning. Father? Father! Anyone here? Duncan! Father! Who is it? (..)1991 Robin Hood: Prince of Thieves