This is an interesting way to describe the difference between Laertes and Hamlet. Laertes's revenge would be considered "hot" because he is very hot-headed upon his return to Denmark and claims that the will stop at nothing to avenge his father's murder. When he first arrives at Elsinore, he is blaming Claudius because he sees it as Claudius's fault for not controlling his crazy step-son, Hamlet. He demands the whole story saying:
I'll not be juggled with:
To Hell, allegiance! vows, to the blackest pit!
I dare damnation. To this point I stand,
That both the worlds I give to negligence,
Let come what comes; only I'll be revenged
Most thoroughly for my father.
He is clearly exclaiming that he isn't thinking of the possible consquences of his actions. He is willing to damn his soul to hell in the process of getting revenge. He won't be loyal to anyone on earth, or God in heaven. These are the kinds of words that would NEVER come from Hamlet!
Hamlet's revenge would be considered cold as it shows to be the opposite of Laertes's behavior. Hamlet desperately wants to exact revenge on Claudius, but he much more thoughtful in his actions and expresses several concerns about the justice of his actions and the need to have proof so that the death of Claudius will be justified. He wants the death to be in a time of sinful behavior so that Claudius's has no chance at heaven. Hamlet doesn't jump to action immediately after the ghost reveals the truth, he takes weeks to finally take action. Hamlet is motivated, but cautious about the consequences of his action. He feels strongly, but doesn't act quickly, therefore his revenge is more cold and calculating.