Dilute solutions of a poly(styrene-b-dimethylsiloxane) diblock copolymer with block molecular weights of 4 and 12 kDa, respectively, were prepared in a series of styrene-selective dialkyl phthalates: dioctyl phthalate (DOP), dibutyl phthalate (DBP), and diethyl phthalate (DEP). The phthalates were chosen because the interfacial tension between the core block and the solvent can be continuously varied by mixing the solvents in varying proportions. The morphologies were characterized by cryogenic transmission electron microscopy (cryo-TEM) and dynamic light scattering (DLS). By increasing the selectivity of the mixed solvent at room temperature the equilibrium micelle morphology changed from spheres (DOP) to cylinders (DBP) to vesicles (DEP). The selectivity of the solvent was then reduced by increasing the temperature, and we observed the reverse transitions: cylinders → spheres (in DBP) and vesicles → cylinders → spheres (in DEP). Since the core block is always above its glass transition temperature (Tg ≈ -123°C), micellar rearrangement was possible within the time scale of the experiment (i.e., minutes). An interesting consequence of these thermotropic transitions is that the viscosity of the solution can be increased upon heating. For example, in the mixed solvent DEP/DBP (1:1), the diblock forms vesicles at room temperature, but when heated, the micelle morphology changes to cylinders and the viscosity of the solution increases by an order of magnitude.