Abstract
Thermal ionization is a critical process at temperatures T > 10 3 K, particularly during star formation. An increase in ionization leads to a decrease in nonideal magnetohydrodynamics (MHD) resistivities, which has a significant impact on protoplanetary disks and protostar formation. We developed an extension of the fast computational ionization method presented in our recent paper to include thermal ionization. The model can be used to inexpensively calculate the density of ions and electrons and the electric charge of each size of grains for an arbitrary size distribution. This tool should be particularly useful for the self-consistent calculation of nonideal MHD resistivities in multidimensional simulations, especially of protostellar collapse and protoplanetary disks.