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]
(..) a wooden knight. Gregor never said a word, he just grabbed his brother by the scruff of his neck and shoved his face into the burning coals. Held him there while the boy screamed, while his face melted. There aren't very many people who know that story. (..)2011 TvShow: Game of Thrones Title: Cripples, Bastards, and Broken Things Season: 1 Episode 4
(..) - They like their bloodshed. They stopped liking it at the end. That was a proper battle. Do you remember Thoros of Myr charging through the breach? With his burning sword? I'll remember that till the day I die. I saw the youngest of the Greyjoy lads at Winterfell. It was like seeing a shark (..)2011 TvShow: Game of Thrones Title: Cripples, Bastards, and Broken Things Season: 1 Episode 4