A thermoforming mold device (1) providing a piece with a thin wall starting with a sheet of thermoplastic material is provided. At least one (3) of two parts of the mold (3, 3′) comprises at least one means (4) of local deformation of a sheet (2′) in the mold (3, 3′) in its closed state, the at least one means (4) comprises a piece of hollow molding with a peripheral edge, which can be connected selectively to a source of suction and can be displaced between a folded position, in which the molding piece is situated in close proximity with the wall of the thermoformed piece, and a deployed position, in which the molding piece is applied under pressure with its peripheral edge against the wall of the thermoformed piece upholding the other part of the mold.