A thermoforming assembly includes a lower mold part (20) and an upper mold part (34). The two mold parts are able to move in a substantially vertical direction between an open position and a closed position. Retaining members (28) are able to hold a sheet of softened thermoplastic (10) in a substantially horizontal mean plane Pm between the two mold parts. The retaining members include a plurality of rods (28) mounted mobile in the lower mold part (20). The rods (28) project out from the lower mold part (20) when the two mold parts (20, 34) are in the open position, to hold the sheet of softened thermoplastic (10) in the substantially horizontal mean plane Pm and accompany it as the mold closes.