A process for the production of a fiber profile (32) that is designed to fill in a space with a nail-head-shaped or half-nail-head-shaped cross-section that originates from the assembly of preforms in a T shape, of which at least one includes a curvature radius at the junction zone of the preforms, includes: supplying powder-coated fibers (28) to a preforming station (30) where the powder is activated and the fibers (28) move into a passage whose shapes are adapted to those of the desired profile, and then making the preformed fibers move into a shaping station (34) where the fiber profile (32) is cooled and shaped by circulating in a cavity whose shapes are adapted to those of the desired profile.