An endodontic instrument for drilling the root canals of a tooth. The instrument comprises a working area for forming and/or shaping and/or cutting the wall of the root canal of the tooth. The working area is provided with a supporting endpiece that can be attached to a manual or mechanically driven mounting. The working area is arranged so as to assume a stowed configuration when the instrument is in an inoperative position to the working position, and vice versa, being cause by a predetermined variation in the temperature of the instrument. To this end, the working area is made from a wire of a metal alloy having shape-memory properties or particular elasticity properties.