How appropriate are the metaphors of fire, steel, and spur to the subject of the speech by Brutus in William Shakespeare's Julius Caesar?

Brutus's imagery in act 2, scene 1, is expressive of the seriousness with which Brutus himself—and presumably all of the conspirators—view the situation that confronts them with regard to Caesar. The historical context in which the drama takes place needs, of course, to be understood in order for us to evaluate Brutus's decision to take part in the assassination.
Roman patricians, and probably many of the plebeians as well, prided themselves on Rome's status as a republic. It was not a democracy as we understand the term, but unlike most political entities in antiquity, Rome was at this time a state not under the authoritarian rule of a king or any one individual. Caesar, in his defiance of the Senate, had changed the situation and set himself up, in the interests of the stability and the survival of Rome, as dictator. In the thinking of Brutus and others, the contradictions inherent in the Roman republic—such as the facts of slavery being a long-standing practice, that Rome had in effect already become an empire (though it was not considered one until the reign of Caesar's grand-nephew Octavian/Augustus was stabilized), the conquering and controlling other peoples—did not come into play. To the conspirators, the situation was tantamount to what it would be today in the U.S. or Britain if the president or prime-minister began unilaterally making decisions in defiance of the Constitution and the established form of government.
Given these desperate conditions, as Brutus and the others saw them, I wouldn't necessarily consider his imagery to be all that extreme or violent. His reference to the "melting hearts of women" comes off rather badly from our perspective, but presumably, Brutus in his way is trying to insure that the others will not back down and that their own resolve (if I may paraphrase while retaining the key words of your question) will be "kindled" by the fire of justice, that their hearts will be "steeled" and that they will be spurred to action. Brutus is depicted as a man of "pure" motives, unlike the other conspirators, when Antony describes him at the play's close. The language Shakespeare gives him is appropriate to that noble, untarnished quality that animates him. But we must judge for ourselves if the cause of the conspirators really was as fully justified as Brutus and the others believe it to have been. This is the key issue at the heart of the drama. Was Caesar's killing the only recourse these men had, the only way of redressing what they considered an injustice? Or was Caesar not the tyrant they believed him? Was he actually, in Antony's words, "the noblest man that ever lived in the tide of times"? This is a question historians have been debating for 2,000 years.