I must admit that that is mostly what I remember from history class. Give me a little bit of time and I will research into it if you wish me to. To add something to it: When I was in school I was a very clear and absolutely strongly believing Catholic. I did not think that the punishment for heresy was inappropriate or something that would put blame on the church given the historical context of the law system. When I think of the power of the church in these ages (they are called the dark ages for a reason) I think of cases like
Canossa. That one might have been the epitome of Catholic rule over the leaders of Europe, but I think I can deduct that other cases in that period, though not as openly shown in history, might have certainly occurred. The people of that day were aware that the church had the power to forgive sins (
#982, p. 256, Cf. Mt 18:21-22;
#986, p. 257;
#1448, p. 363-364, chapter on the sacrament of penance and reconciliation) which can be a very powerful tool. Though I personally do not agree with that anymore, it certainly had an effect on the people of that day and age. Opposition to the church would have led to excommunication (see Canossa). For a ruler of that time this meant to loose basically all they had including their authority and power. Whether or not they liked it, they did prescribe the death penalty for unrepentant heretics and for heretics who repeatedly fell back into heresy and repented of it as you could see in the Summa. Whatever their attitude towards killing someone, the result is the same.
In the historical context of a rather elaborate and mostly cruel justice system, just burning someone seems oddly merciful.