Diblock copolymer vesicles are prepared via RAFT dispersion polymerization directly in mineral oil. Such vesicles undergo a vesicle-to-worm transition on heating to 150 degrees C, as judged by TEM and SAXS. Variable-temperature H-1 NMR spectroscopy indicates that this transition is the result of surface plasticization of the membrane-forming block by hot solvent, effectively increasing the volume fraction of the stabilizer block and so reducing the packing parameter for the copolymer chains. The rheological behavior of a 10% w/w copolymer dispersion in mineral oil is strongly temperature-dependent: the storage modulus increases by five orders of magnitude on heating above the critical gelation temperature of 135 degrees C, as the non-interacting vesicles are converted into weakly interacting worms. SAXS studies indicate that, on average, three worms are formed per vesicle. Such vesicle-to-worm transitions offer an interesting new mechanism for the high-temperature thickening of oils.