DIBLOCK copolymers, comprised of two distinct homopolymers covalently bonded together at one end, undergo a transition on cooling from a state in which the segments of the blocks are homogeneously mixed to one in which they are segregated locally(1,2). This microphase separation is driven by the enthalpy of unfavourable interactions between segments. Here we report the microphase separation of a diblock copolymer melt on heating. Similar in nature to the lower critical solution temperature seen in polymer mixtures, this lower critical ordering transition is driven by entropic factors-specifically, by a negative volume change on mixing of the blocks. The transition to the microphase-separated state alters the theological and mechanical properties of the copolymer markedly, the material gaining a non-zero equilibrium modulus above the ordering transition. This suggests potential technological applications of these copolymer systems as ’smart’ materials.