An apparatus (1) for processing container closures (2) comprises a sterilization unit (3), having a sterilization module (7) with means for spraying on the closures (2) a hot sterilization fluid, a capping unit (4), having screwing means active on the closures (2) for connecting them on correspondent containers, applying a predetermined torque, a guide member (5) configured in such a way to allow a plurality of closures (2) to be arranged therein and connected to the sterilization unit (3) and to the capping unit (4) to guide the closures (2) from the sterilization unit (3) to the capping unit (4), and means (13) for regulating the temperature of the closures (2) arranged in the guide member (5), to provide that the closures (2) have a predetermined desired temperature in the capping unit (4).A method for processing container closures (2) comprises the following steps: sterilizing the closures (2) by spraying on the closures (2) a hot sterilization fluid, transferring the closures (2) from a sterilization unit (3) to a capping unit (4), by means of a guide member (5) interposed therein, screwing the closures (2) for connecting them on correspondent containers, applying a predetermined torque to the closures (2) in the capping unit (4), and regulating the temperature of the closures (2) arranged in the guide member (5), to provide that the closures (2) have a predetermined desired temperature in the capping unit (4).