A flat laminate element made of thermoplastic is hot-formed in a two-stage method. In a first stage, the flat laminate which includes film(s) and/or panels(n) is placed on a flat frame-shaped pallet and is heated to a forming temperature in a heating zone between two flat heat screens in a contactless manner. The edge zone of the hot flat laminate element lies on the pallet such that the laminate piece cannot be clamped in a first laminate direction but rather can be slide on the pallet in this direction. Two non-flat rigid contours which are identical or largely identical act on two opposing parallel laminate edge sections uniaxially and perpendicularly to the laminate plane and only in the first laminate direction, i.e. monodirectionally, and shape the entire heated laminate element into a monodirectionally molded blank.