Mixtures of gas-phase hydrogen isotopologues (diatomic combinations of protium, deuterium, and tritium) can be separated using columns containing a solid such as palladium that reversibly absorbs hydrogen. A temperature-swing process can transport hydrogen into or out of a column by inducing temperature-dependent absorption or desorption reactions. We consider two designs: a thermal cycling absorption process, which moves hydrogen back and forth between two columns, and a simulated moving bed (SMB), where columns are in a circular arrangement. We present a numerical mass and heat transport model of absorption columns for hydrogen isotope separation. It includes a detailed treatment of the absorption−desorption reaction for palladium. By comparing the isotope concentrations within the columns as a function of position and time, we observe that SMB can lead to sharper separations for a given number of thermal cycles by avoiding the remixing of isotopes.