No, we certainly do not burn people alive. To give a short version of events: in Thedas, magic can be a very dangerous force, and mages are in danger of demonic possession. For ages, mages have been confined to the Circles of Magi, taken from their homes as soon as they exhibit signs of power and brought their to be trained, and also contained. The Knights Templar were created to both protect these mages, and to protect others from the ones who succumb to demons. The Templars and Mages both fell under the jurisdiction of the Chantry, the largest religious organization in Thedas. In recent years, war broke out between the Mages and Templars, and the Chantry weakened. A conclave was called to discuss peace, but was attacked by demons, killing nearly every leader of all three organizations. In the wake of this mass destruction and war, the Inquisition was reformed to restore order. From what I understand, its previous incarnation had some of the religious brutality of the one you describe. Ours is just trying to set a mad world back to rights and hopefully build one that will not lead to another such war.