No they weren’t. You really need to study up a bit. Temporal punishments were meted out by temporal authorities.
Because, you see, there was a distinction between two two forms of authority.
You’ve read too much Enlightenment cavilling at the Ancien Regime (during Absolutism) and too much Dan Brown.
First of all, I’ve never read any Dan Brown at all, so I do expect an apology for that slander. Secondly, if the Inquisitions were established and authorized by the Papal Bulls, you cannot divorce them from Ecclesiastical Authority. Charles Manson didn’t actually murder anyone in the Tate-LaBianca killing spree, but he gave the order for it to happen, and every rational person agrees that he is the one who bears the lion’s share of the blame in the matter.