The preform is formed by an upper neck which maintains unchanged its form in the final object and a hollow body, joined to the neck. The method foresees the insertion, within a matrix cavity, of a metered body of polymeric material whose mass is metered according to a reference value, and the subsequent pressure insertion of a punch within the matrix cavity until it closes the mold's molding chamber, the punch conferring the shape to the inner surface of the preform and the matrix having an inner surface which confers the shape to the outer surface of the preform. According to the invention, in the molding of the preform, the error of the mass of the metered body with respect to the reference value is distributed in the hollow body, which undergoes a subsequent hot deformation until it achieves the final shape. In the mold, the matrix comprises at least one deformable wall (31) whose inner surface defines at least part of the inner surface of the matrix part intended to give form to the hollow body of the preform, said deformable wall (31) having, at least in part, a relatively thin thickness which permits it to be elastically deformed under the pressure of the polymeric material in the final preform molding step, thereby varying the thickness of the hollow body.