A process for the selective additive manufacture of a three-dimensional object from a layer of powder comprises: applying a layer of additive manufacturing powder to a support or to a previously consolidated layer, emitting a laser beam onto a first point of the layer of additive manufacturing powder so as to consolidate a first zone of the layer of powder comprising the first point, adjusting a power of the laser beam depending on an estimated temperature variation of the layer of powder at a second point, separate from the first point, and emitting a laser beam onto the second point with the adjusted power so as to consolidate a second zone of the layer of powder comprising the second point, the emission of the laser beam onto the first point and onto the second point being temporally separated by the predetermined time interval.