Impact bombardment during the first billion years after the formation of the Moon produced at least several tens of basins. The Gravity Recovery and Interior Laboratory (GRAIL) mission mapped the gravity field of these impact structures at significantly higher spatial resolution than previous missions, allowing for detailed subsurface and morphological analyses to be made across the entire globe. GRAIL-derived crustal thickness maps were used to define the regions of crustal thinning observed in centers of lunar impact basins, which represents a less unambiguous measure of a basin size than those based on topographic features. The formation of lunar impact basins was modeled numerically by using the iSALE-2D hydrocode, with a large range of impact and target conditions typical for the first billion years of lunar evolution. In the investigated range of impactor and target conditions, the target temperature had the dominant effect on the basin subsurface morphology. Model results were also used to update current impact scaling relationships applicable to the lunar setting (based on assumed target temperature). Our new temperature-dependent impact-scaling relationships provide estimates of impact conditions and transient crater diameters for the majority of impact basins mapped by GRAIL. As the formation of lunar impact basins is associated with the first ~700 Myr of the solar system evolution when the impact flux was considerably larger than the present day, our revised impact scaling relationships can aid further analyses and understanding of the extent of impact bombardment on the Moon and terrestrial planets in the early solar system.