We report the synthesis of colloidal CdSe/Cu(3)P/CdSe nanocrystal heterostructures grown from hexagonal Cu(3)P platelets as templates. One type of heterostructure was a sort of "coral", formed by vertical pillars of CdSe grown preferentially on both basal facets of a Cu(3)P platelet and at its edges. Another type of heterostructure had a "sandwich" type of architecture, formed by two thick, epitaxial CdSe layers encasing the original Cu(3)P platelet. When the sandwiches were annealed under vacuum up to 450 °C, sublimation of P and Cd species with concomitant interdiffusion of Cu and Se species was observed by in situ HR- and EFTEM analyses. These processes transformed the starting sandwiches into Cu2Se nanoplatelets. Under the same conditions, both the pristine (uncoated) Cu(3)P platelets and a control sample made of isolated CdSe nanocrystals were stable. Therefore, the thermal instability of the sandwiches under vacuum might be explained by the diffusion of Cu species from Cu(3)P cores into CdSe domains, which triggered sublimation of Cd, as well as out-diffusion of P species and their partial sublimation, together with the overall transformation of the sandwiches into Cu(2)Se nanocrystals. A similar fate was followed by the coral-like structures. These CdSe/Cu(3)P/CdSe nanocrystals are therefore an example of a nanostructure that is thermally unstable, despite its separate components showing to be stable under the same conditions.