Green’s Dictionary of Slang

1. to kill, to murder.

1863		in A. Cook Armies of the Streets (1974) 117: You shut up or we will cool [you] off.
1917		‘Whale Song’ in J.J. Niles Singing Soldiers (1927) 11: The mills bomb ricocheted and cooled Jonah off instead.
1920		A. Baer Putting ‘Em Away 7 Dec. [synd. col.] Mike cooled off so many Germans that the allies had to invent new medals for him.
1938		D. Runyon ‘What, No Butler?’ in Runyon on Broadway (1954) 387: Somebody gets in here and cools off Mr. Justin Veezee.
1947		H.E. Helseth Chair for Martin Rome 126: You don’t cool off Two-Scar, I will.
1956		H. Ellison ‘I’ll Bet You a Death’ in Deadly Streets (1983) 39: You cool off a harness boy, you get Cherry.
1963		C. Cooper Jr ‘Yet Princes Follow’ in Black! (1996) 184: One of his women cooled him off with four or five airholes.

2. to knock out, to subdue with physical force.

1931		D. Maurer ‘Carnival Cant’ in AS VI:5 330: cool him off, v.phr. To take a ‘monkey’ aside and console him when he has lost so he will not complain to the police or cause a disturbance [...] The ‘cooling’ process sometimes consists of blackjacking.
1940		W.R. Burnett High Sierra in Four Novels (1984) 288: Roy had to cool off a couple of the tougher ones [i.e. prisoners] and ended up in solitary for his trouble.