A method of manufacturing an impregnated fibrous material including a fibrous material made of continuous fibers and at least one thermoplastic polymer matrix, the method including pre-impregnating the fibrous material while it is in the form of a roving or several parallel rovings with the thermoplastic material and heating the thermoplastic matrix for melting, or maintaining in the molten state, the thermoplastic polymer after pre-impregnation, the at least one heating step being carried out by means of at least one heat-conducting spreading part (E) and at least one heating system, with the exception of a heated calendar, the roving or the rovings being in contact with part or all of the surface of the at least one spreading part (E) and partially or wholly passing over the surface of the at least one spreading part (E) at the level of the heating system.