The morphology of rf-sputtered films of the wide bandgap semiconductor InN on a variety of substrates over a range of temperatures have been studied by X-ray diffraction (XRD) and scanning tunneling microscopy (STM). For films deposited on fused quartz and the (111) face of silicon, there is a transition from an off-normal inclination to a fully textured (0001) film with increasing substrate temperature. In contrast, films deposited on the (0001) face of sapphire are textured or heteroepitaxial depending on the substrate temperature. For the heteroepitaxial domains, the rotation of the reciprocal lattice of InN by 30° to that of the sapphire substrate was established by X-ray precession photography. Finally, STM has proven to be a practicable method for non-destructively determining the substrate and temperature dependence of the grain size and surface roughness of these textured and heteroepitaxial films.