A detailed microscopic study of the temperature dependence of the shapes of
some rare-earth nuclei is made in the relativistic mean field theory. Anal
yses of the thermal evolution of the single-particle orbitals and their occ
upancies leading to the collapse of the deformation are presented. The role
of the nonlinear sigma field on the shape transition in different nuclei i
s also investigated; in its absence the shape transition is found to be sha
rper.