St. Thomas Aquinas (1225-1274) is highly respected as an author and teacher in the Roman Catholic Church. He wrote on nearly the entire range of theology and philosophy. His main works were Summa contra Gentiles and Summa Theologiae. He was canonized as a Catholic saint in 1323, proclaimed a doctor of theology in 1567, and named patron of Catholic schools and education on January 28, 1880.
Here from Summa Theologiae is Thomas Aquinas' definition of a heretic:
Aquin.: SMT SS Q A R.O. 3 Para. 1/1
Reply OBJ 3: As Augustine says (Ep. xliii) and we find it stated in the Decretals (xxiv, qu. 3, can. Dixit Apostolus): "By no means should we accuse of heresy those who, however false and perverse their opinion may be, defend it without obstinate fervor, and seek the truth with careful anxiety, ready to mend their opinion, when they have found the truth," because, to wit, they do not make a choice in contradiction to the doctrine of the Church.
Accordingly, certain doctors seem to have differed either in matters the holding of which in this or that way is of no consequence, so far as faith is concerned, or even in matters of faith, which were not as yet defined by the Church; although if anyone were obstinately to deny them after they had been defined by the authority of the universal Church, he would be deemed a heretic.
This authority resides chiefly in the Sovereign Pontiff. For we read [*Decret. xxiv, qu. 1, can. Quoties]: "Whenever a question of faith is in dispute, I think, that all our brethren and fellow bishops ought to refer the matter to none other than Peter, as being the source of their name and honor, against whose authority neither Jerome nor Augustine nor any of the holy doctors defended their opinion."
Hence Jerome says (Exposit. Symbol [*Among the supposititious works of St. Jerome]): "This, most blessed Pope, is the faith that we have been taught in the Catholic Church. If anything therein has been incorrectly or carelessly expressed, we beg that it may be set aright by you who hold the faith and see of Peter. If however this, our profession, be approved by the judgment of your apostleship, whoever may blame me, will prove that he himself is ignorant, or malicious, or even not a catholic but a heretic."
So according to Thomas Aquinas, the issue at stake is the defined doctrines and dogma of the Roman Catholic Church. If you knowingly contradict the Papacy and doctrines as the Pope defines them, then you are a classed as a heretic. Following are four possible observations about tolerating heretics...
Aquin.: SMT SS Q A Thes. Para. 1/1
Whether heretics ought to be tolerated?
Aquin.: SMT SS Q A Obj. 1 Para. 1/1
OBJ 1: It seems that heretics ought to be tolerated. For the Apostle says (2 Tim. 2:24,25): "The servant of the Lord must not wrangle . . . with modesty admonishing them that resist the truth, if peradventure God may give them repentance to know the truth, and they may recover themselves from the snares of the devil." Now if heretics are not tolerated but put to death, they lose the opportunity of repentance. Therefore it seems contrary to the Apostle's command.
Aquin.: SMT SS Q A Obj. 2 Para. 1/1
OBJ 2: Further, whatever is necessary in the Church should be tolerated. Now heresies are necessary in the Church, since the Apostle says (1 Cor. 11:19): "There must be . . . heresies, that they . . . who are reproved, may be manifest among you." Therefore it seems that heretics should be tolerated.
Aquin.: SMT SS Q A Obj. 3 Para. 1/1
OBJ 3: Further, the Master commanded his servants (Mt. 13:30) to suffer the cockle "to grow until the harvest," i.e. the end of the world, as a gloss explains it. Now holy men explain that the cockle denotes heretics. Therefore heretics should be tolerated.
Aquin.: SMT SS Q A OTC Para. 1/1
On the contrary, The Apostle says (Titus 3:10,11): "A man that is a heretic, after the first and second admonition, avoid: knowing that he, that is such an one, is subverted."
And now, Thomas Aquinas' opinion on what should be done with heretics ...
Aquin.: SMT SS Q A Body Para. 1/2
I answer that, With regard to heretics two points must be observed: one, on their own side; the other, on the side of the Church. On their own side there is the sin, whereby they deserve not only to be separated from the Church by excommunication, but also to be severed from the world by death. For it is a much graver matter to corrupt the faith which quickens the soul, than to forge money, which supports temporal life. Wherefore if forgers of money and other evil-doers are forthwith condemned to death by the secular authority, much more reason is there for heretics, as soon as they are convicted of heresy, to be not only excommunicated but even put to death.
Aquin.: SMT SS Q A Body Para. 2/2
On the part of the Church, however, there is mercy which looks to the conversion of the wanderer, wherefore she condemns not at once, but "after the first and second admonition," as the Apostle directs: after that, if he is yet stubborn, the Church no longer hoping for his conversion, looks to the salvation of others, by excommunicating him and separating him from the Church, and furthermore delivers him to the secular tribunal to be exterminated thereby from the world by death. For Jerome commenting on Gal. 5:9, "A little leaven," says: "Cut off the decayed flesh, expel the mangy sheep from the fold, lest the whole house, the whole paste, the whole body, the whole flock, burn, perish, rot, die. Arius was but one spark in Alexandria, but as that spark was not at once put out, the whole earth was laid waste by its flame."
Submission to their alleged authority has always been the primary concern of the Roman Catholic Church. History well documents the bloodshed that resulted from thinking like that demonstrated above, when people dared to read the Bible for themselves and follow its precepts and doctrines without interference from the Catholic Church, even daring to reject the pronouncements and decrees of the Pope himself. The death of these martyrs of the faith at Catholic hands is also recorded prophetically in the Bible-Rev 17:6 And I saw the woman drunken with the blood of the saints, and with the blood of the martyrs of Jesus: and when I saw her, I wondered with great admiration.
Here is the above section of Summa Theologica online at the New Advent Catholic Supersite.