The present invention relates to a process for producing a diblock copolymer comprising the reaction of at least one aromatic polyester having a melting point in the range from 160?C. to 350?C. and at least one polymer diol having a melting point of less than 100?C. at a temperature of greater than 200?C. to obtain a mixture (G-a); and the reaction of the mixture (G-a) with at least one diisocyanate, wherein the diisocyanate is employed in a molar amount of at least 0.9 based on the alcohol groups of the polymer diols. The present invention further relates to diblock copolymers obtained or obtainable according to such a process and to the use of such diblock copolymers for producing extruded, injection molded and pressed articles and also foams, cable sheaths, hoses, profiles, drive belts, fibers, nonwovens, films, moldings, plugs, housings, damping elements for the electricals industry, automotive industry, mechanical engineering, 3-D printing, medicine and consumer goods.