We produce a set of scaling laws for basin-sized impacts using data from a suite of lunar basin numerical models. The results demonstrate the importance of preimpact target temperature and thermal gradient, which are shown to greatly influence the modification phase of the impact cratering process. Impacts into targets with contrasting thermal properties also produce very different crustal and topographic profiles for impacts of the same energy. Thermal conditions do not, however, significantly influence the excavation stage of the cratering process; results demonstrate, as a consequence of gravity-dominated growth, that transient crater radii are generally within 5% of each other over a wide range of thermal gradients. Excavation depth-to-diameter ratios for the basin models (~0.12) agree well with experimental, geological, and geophysical estimates, suggesting basins follow proportional scaling. This is further demonstrated by an agreement between the basin models and Pi- scaling laws based upon first principles and experimental data. The results of this work should also be applicable to basin-scale impacts on other silicate bodies, including the Hadean Earth.