We have investigated the morphology of heterostructured GaP-GaAs nanowires grown by metal-organic vapor-phase epitaxy as a function of growth temperature and V/III precursor ratio. The study of heterostructured nanowires with transmission electron microscopy tomography allowed the three-dimensional morphology to be resolved, and discrimination between the effect of axial (core) and radial (shell) growth on the morphology. A temperature- and precursor-dependent structure diagram for the GaP nanowire core morphology and the evolution of the different types of side facets during GaAs and GaP shell growth were constituted.