Actually, I was always taught that Satan was unsure of Christ's divinity. He did not ever consider the fact that God could actually appear with such humility. Hence, Our Lord defeated Satan through the virtue of humility, the one virtue that he (satan) lacked while he was an archangel. He fell into the sin of pride as an archangel, ultimately leading to his fall from the heavens. Consider this: If Satan did really know that Christ was the Incarnate Word of God, then why would he ever possess Judas, and lead him to betraying Our Savior? If this was the case, we would say that Satan defeated himself, and not that Our Savior defeated him by his humility and death on the holy wood of the cross.
Same idea applies to the temptation of Christ. Had Satan indeed been sure of the Divinity of Christ, he would never have bothered to tempt him. The devil knows quite well that God is without sin, and this can never change. He tempted Christ while baffled, unsure of whether he was a prophet, or was he indeed the Logos of God.