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1.
When someone has thirst for a cock, or desires to have penis in around his/her face.

To thirst for cock.

The uncontrollable impulse to give fellatio to a cock, regardless of size, shape, or color.

In a member of the male sex, cockthirst can be considered homosexual and mad 'mo.

In a member of the female sex, excessive cockthirst can be considered promiscuous and slutty.
Man: MY COCKTHIRST CONSUMES REASON AND CAUSES ME TO CONSUME PENIS

Man2: Yo that's mad gay for no reason bud

Woman1: I have the cockthirst. Let's go find male genitalias to fellatio.

Man2: LETS GOOO

Man1: Okay, unzip =]

Woman2: This is promiscuous and slutty, whores.
by Speeding Ginger April 17, 2010
 
2.
Used to denote an occassion when a homosexual is sexually frustrated and in need of some cock action.

Thought to have originated in Glasgow
Mike: "Hey Robbie have you seen Richie today?"

Robbie: "Yeah he is in one fucking bad mood, he definately has the cock thirst"

Mike: "I will stay clear of him or he might try and hump me"

Robbie: "I would too. He is one crazy, sex hungry, gay fucker!"
by Garry Hamilton July 07, 2006