A method and forming tool for hot forming and press hardening plate-shaped or preformed workpieces of sheet steel, wherein the workpiece is heated to a temperature above the austenitisation temperature and is then formed and quenched in a cooled forming tool having a punch and a female mold, wherein the female mold is coated in its drawing edge region with material in a material-uniting manner and/or is provided there with at least one insert part having a thermal conductivity at least 10 W/(m*K) lower than the thermal conductivity of the portion of the female mold adjacent to the drawing edge region and comes into contact with the workpiece when said workpiece is being hot formed and press hardened, the surface of the material having a transverse dimension within the range of 1.6 times to 10 times the positive radius of the female mold.