Green’s Dictionary of Slang

1. (orig. US) very excited.

1934

H. Miller Tropic of Cancer (1963) 140: You get all burned up about nothing . . . about a crack with hair on it.

2. (orig. US, also burnt up) extremely angry.

1923		H.C. Witwer Fighting Blood 173: When Frankie finds out [...] that I fooled him into losing a chance to knock me with a punch at any time after that, he’s burnt up! [Ibid.] 274: By the time I got done telling Mr. Brock what’s what he’s as burnt up as I am.
1928		W. Winchell Your Broadway & Mine 7 Dec. [synd. col.] Those who profess to be ‘in the know’ are being burned up and knocked cold [etc].
1934		J.M. Cain Postman Always Rings Twice (1985) 13: A guy came along that was all burned up because somebody had pasted a sticker on his wind wing.
1937		(con. 1905–25) E.H. Sutherland Professional Thief (1956) 171: That mob was happy because they were able to make suckers out of a couple of expert boosters, and these two were burned up about it.
1937		P. Cheyney Dames Don’t Care (1960) 13: She [...] looks like she could bite a snake’s head off. She’s permanently burned up.
1947		I. Shulman Amboy Dukes 98: I’m just burned up because she stood you up.
1951		M. Spillane One Lonely Night 107: Did you ever see a guy who was burned up at his wife?
1960		J.P. Donleavy Fairy Tales of N.Y. III i: He says if he ever gets you in the ring he’ll kill you for some of the other things you said. He gets really burned up.
1965		J. Thompson Texas by the Tail (1994) 9: He was pretty burned up himself. She’d been late on the take-out.
1985		S. Berkoff West in Decadence and Other Plays (1985) 123: Right burnt up he was about it.
1999		J. Ridley Love Is a Racket 372: You’re all burned up inside ’cause Moe has a piece of me you can never touch.

3. see burned (at) adj.

4. see burned out adj.¹ (1)