Process for the production of a fiber profile (32) that is designed to fill in a space (14, 26) with a nail-head-shaped or half-nail-head-shaped cross-section that originates from the assembly of preforms (10, 12, 12′, 20, 22, 24) in a T shape, of which at least one comprises a curvature radius at the junction zone of said preforms, characterized in that it consists in supplying powder-coated fibers (28) to a preforming station (30) where said powder is activated and said fibers (28) move into a passage (62) whose shapes are adapted to those of the desired profile, and then in making said preformed fibers move into a shaping station (34) where said fiber profile (32) is cooled and shaped by circulating in a cavity (66) whose shapes are adapted to those of the desired profile.