An extensive investigation of InN overlayers on AlN‐buffered (00.1) sapphire by reactive magnetron sputtering has been undertaken and the dependencies of several basic materials properties (film thickness, development and quality of heteroepitaxy, film morphology, and electrical transport) on such key deposition parameters such as the growth temperatures of the insulating AlN buffer layer and the InN overlayer and their thicknesses have been determined. Three prominent effects of the AlN buffer layer are (1) the stabilization of heteroepitaxial growth over a broad range of film and buffer layer growth temperatures; (2) the attainment of a higher Hall mobility (up to 60 cm2/V s) over much of the same range; and, (3) the retention of heteroepitaxial growth, higher Hall mobility, and pseudo‐two‐dimensional growth even in the limit of an InN layer of ∼40 A˚. In the context of a structure‐zone model, the AlN buffer layer is projected to effectively raise the growth temperature of the InN thin film. The increase in effective growth temperature is, however, insufficient to overcome low atomic and cluster mobility and to achieve single‐crystal InN thin film growth.