We develop a method to compute thermally mediated transition rates between the ground state and long-lived isomers in nuclei. We also establish criteria delimiting a thermalization temperature above which a nucleus may be considered a single species and below which it must be treated as two separate species: a ground-state species and an astrophysical isomer ("astromer") species. Below the thermalization temperature, the destruction rates dominate the internal transition rates between the ground state and the isomer. If the destruction rates also differ greatly from one another, the nuclear levels fall out of or fail to reach thermal equilibrium. Without thermal equilibrium, there may not be a safe assumption about the distribution of occupation probability among the nuclear levels when computing nuclear reaction rates. In these conditions, the isomer has astrophysical consequences and should be treated as a separate astromer species which evolves separately from the ground state in a nucleosynthesis network. We apply our transition-rate methods and perform sensitivity studies on a few well-known astromers. We also study transitions in several other isomers of likely astrophysical interest. © 2020. The American Astronomical Society. All rights reserved.