The invention relates to a method for producing a component from a medium manganese flat steel product having 4 to less than 10 wt. % Mn, 0.0005 to 0.9 wt. % C, 0.02 to 10 wt. % Al, the remainder iron, including unavoidable steel-accompanying elements, and having a TRIP effect at room temperature. In order to produce a component, which is distinguished by very high strengths and an increased residual strain and re-shaping capacity, the flat steel product, according to the invention, is re-shaped by at least one re-shaping step to form a component and, before and/or during and/or after the at least one re-shaping step, the flat steel product is cooled down to a temperature of the flat steel product of less than room temperature to −196° C. The invention further relates to a component produced by this method and to a use for said components.