Catholics Church and the Burning of Heretics

It's quite unfortunate that some catholics believe that the church approved the burning of heretics. In the face of false accusations by protestants, weak catholics tend to summit to these allegations without uttering a word in defence. I've even heard a protestant say that Galileo was burnt by the Church. Of course this is false for Galileo wasn't burnt at stake. Anyway, this is a topic for another day.
The following is an explanation by St. Thomas Aquinas on the Church's actions with regard to heretics.

"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 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.
"On the part of the Church, however, there is mercy which looks to the conversion of the Wonderer, 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."