ZnO nanobelts may grow with their polar axis perpendicular to growth direction. Heterostructured nanobelts therefore contain hetero-interfaces along the polar axis of ZnO where polarisation mismatch may induce electron confinement. These interfaces run along the length of the nanobelts. Such heterostructure nanobelts are grown by molecular beam epitaxy and TEM images confirm the core-shell structure. The effects of shell-growth temperature on nano-heterostructures is investigated using photoluminescence and secondary ion mass spectrometry in a focussed ion-beam microscope with Ne+ as the primary ion beam. We perform low temperature photoluminescence on ensembles of such heterostructures and single nanostructures. We show how single nanobelts have photoluminescence spectra rich in features and attribute these to band misalignment at ZnO/ZnMgO interfaces embedded within nano-heterostructures.