The device comprises: a two-for-one twisting spindle supporting a yarn winding which is twisted or cabled via a second yarn; a mechanism for pulling the yarn in order to cancel the tension resulting from the twisting or cabling operation; a heater for heating the yarn followed by a cooling area; and a mechanism for coiling the yarn. The heater comprises at least one cup-shaped element which is associated with a return guide enabling the yarn to be wound. The cup-shaped element is brought to a specific temperature and is positively driven in a state of rotation.