Branched nanostructures are of great interest because of their promising optical and electronic properties. For successful and reliable integration in applications such as photovoltaic devices, the thermal stability of the nanostructures is of major importance. Here the different domains (CdSe cores, CdS pods) of the heterogeneous octapods are shown to have different thermal stabilities, and heating is shown to induce specific shape changes. The octapods are heated from room temperature to 700 degrees C, and investigated using (analytical and tomographic) transmission electron microscopy (TEM). At low annealing temperatures, pure Cd segregates in droplets at the outside of the octapods, indicating non-stochiometric composition of the octapods. Furthermore, the tips of the pods lose their faceting and become rounded. Further heating to temperatures just below the sublimation temperature induces growth of the zinc blende core at the expense of the wurtzite pods. At higher temperatures, (500700 degrees C), sublimation of the octapods is observed in real time in the TEM. Three-dimensional tomographic reconstructions reveal that the four pods pointing into the vacuum have a lower thermal stability than the four pods that are in contact with the support