The apparent thermorheological simplicity of disordered diblocks is reconciled with the failure of time-temperature superposition of corresponding miscible blends by examining the relaxation of the constituent blocks using rheo-optical techniques. Diblocks of 1,4-polyisoprene (PIP) and poly-vinylethylene (PVE) are examined over a range of temperatures for two compositions (phi(PIP) = 0.25 and 0.75). Unlike blends of PIP and PVE, the block copolymers appear to obey time-temperature superposition on the basis of their viscoelastic properties. However, departure from thermorheological simplicity is exposed in their stress-optical behavior. In particular, the copolymer rich in the high T-g component (phi(PIP) = 0.25) shows distinct temperature dependencies for the individual blocks, in accord With the behavior of PIP/PVE blends. The block copolymer rich in the low T-g component (phi(PIP) = 0.75) is thermorheologically simple because both blocks have similar monomeric friction coefficients xi(o,PVE) approximate to xi(o,PIP), again in accord with prior results on PIP/PVE blends. The failure of time-temperature superposition in these diblocks was not previously observed because the change in xi(o,PVE)/xi(o,PIP) with temperature produces subtle changes in the overall relaxation spectrum relative to a linear chain of uniform friction.