  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.
