System (2) for automatically applying a coating element (4) to a support surface comprises a heating device (1) for applying the coating element (4) along an application path of the support surface, by administration of heat obtained by the Joule effect, comprising a first electrode (5) and a second electrode (6) which can be connected to an electric power generator and are configured to form a part of an electric circuit, a portion of the coating element (4) being able to be arranged between the first electrode (5) and the second electrode (6), so as to close the electric circuit, such that the Joule effect heats the portion of the coating element (4) following a flow of current in the electric circuit, the overall configuration of the heating device being such that the first electrode (5) and the second electrode (6) are able to be moved with respect to the coating element (4) during application of the coating element (4) to the support surface, and an automatic movement device (3) being able to move the device (1) along a path for applying the coating element (4) to the support surface.