<p>Hot deforming press comprises an upper tool (2) and a lower tool (3) with molding jaws (6, 7) and supporting jaws which can be displaced relative to each other. The supporting jaws lie on the molding jaws in a blocking position (B) and are spaced from the molding jaws in a cooling position (K) so that a cooling gap is formed between the molding and supporting jaws.</p>