  A systematic study of the temperature dependence of the shapes and pairing
gaps of some isotopes in the rare-earth region is made in the relativistic
Hartree-BCS theory. Thermal response to these nuclei is always found to lead to
a phase transition from the superfluid to the normal phase at a temperature
$T_{\Delta}\sim 0.4 - 0.8$ MeV and a shape transition from prolate to spherical
shapes at $T_c\sim 1.0 - 2.5$ MeV. These shape transition temperatures are
appreciably higher than the corresponding ones calculated in the
non-relativistic framework with the pairing plus quadrupole interaction. Study
of nuclei with continued addition of neutron pairs for a given isotope shows
that with increased ground state deformation, the transition to the spherical
shape is delayed in temperature. A strong linear correlation between
$T_{\Delta}$ and the ground state pairing gap $\Delta^0$ is observed; a well-
marked linear correlation between $T_c$ and the ground state quadrupole
defromation $\beta_2^{0}$ is also seen. The thermal evolution of the
hexadecapole deformation is further presented in the paper.
