  We present finite temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations
for the tin isotope chain to study the dependence of pseudospin on the nuclear
temperature. In the FTDHB calculation, the density dependence of the
self-consistent relativistic mean fields, the pairing, and the vapor phase that
takes into account the unbound nucleon states are considered self-consistently.
The mean field potentials obtained in the FTDHB calculations are fit by
Woods-Saxon (WS) potentials to examine how the WS parameters are related to the
energy splitting of the pseudospin pairs as the temperature increases. We find
that the nuclear potential surface diffuseness is the main driver for the
pseudospin splittings and that it increases as the temperature grows. We
conclude that pseudospin symmetry is better realized when the nuclear
temperature increases. The results confirm the findings of previous works using
RMF theory at $T=0$, namely that the correlation between the pseudospin
splitting and the parameters of the Woods-Saxon potentials implies that
pseudospin symmetry is a dynamical symmetry in nuclei. We show that the
dynamical nature of the pseudospin symmetry remains when the temperature is
considered in a realistic calculation of the tin isotopes, such as that of the
Dirac-Hartree-Bogoliubov formalism.
