A method for preparing composite parts, including a step of depositing at least one band of fibrous material impregnated with a thermoplastic polymer on a substrate, by means of a main heating system selected from the following two systems: a preheating system (1) and a heating system (2), in combination with at least one secondary heating system selected from: a heating system (3), a post-heating system (4), a heating system (5), and a preheating system (6), or by means of the two main heating systems (1) and (2), the substrate being previously devoid of any deposited band or comprising at least one band n−1 of said fibrous material, the thermoplastic polymer being amorphous, with a Tg such that Tg≥80° C., or semicrystalline, with a Tm≥150° C.