II. Good works as well as integrity of faith is required in a priest.
But you see, venerable Emperor, and clearly understand, that in the person, whose excommunication is contemplated, it is not only the integrity of his faith that must be considered; for even if that could be purged by any punishments and confessions, and completely restored by any conditions, yet the wicked and bloody deeds that have been committed can never be done away by the protestations of plausible words: because in God's pontiff, and particularly in the priest of so great a church, the sound of the tongue and the utterance of the lips is not enough, and nothing is of avail, if God makes proclamation with His voice and the mind is convicted of blasphemy. For of such the Holy Ghost speaks by the Apostle, “having an appearance of godliness, but denying the power thereof,” and again elsewhere, “they profess that they know God, but in deeds they deny Him.” And hence, since in every member of the Church both the integrity of the true Faith and abundance of good works is looked for, how much more ought both these things to predominate in the chief pontiff, because the one without the other cannot be in union with the Body of Christ.
Source: Letters (New Advent)