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1.
Slightly adulterated nickname of a particular elitist british hacker from manchester, some of whose antics were widely reported by the press in the 90s.
Hacker A: Hey who's that skinny cunt doing lines in the corner and kickbanning ppl on irc?

Hacker B: Oh yeah thats Cockfire, britains most notorious whacker.
by auldephuker March 02, 2011
 
2.
When a man's cum burns the inside of his penis and often the vagina or anus of his partner
"I tried fucking yesterday, but i had cock fire."
by cyp2il September 02, 2008
 
3.
To be horny,
named after the description of a male's penis to be "on fire" when in need of a sexual fix.
Alf: Damn I got me a case of the Cock-Fire, come over here and fix that.
Sarah: Roger.
by Wolven December 27, 2005
 
4.
when yur fucking a girl that can no longer get wet, and the friction builds up so quick that yur dick and her puss become aflame
hey bitch look at my cockfire.
your dry puss has set my bush on fire, and it smells like shit!!
by matt March 11, 2005