The thermal evolution of the shell-correction energy is investigated for de
formed nuclei using Strutinsky prescription in a self-consistent relativist
ic mean-field framework. For temperature independent single-particle states
corresponding to either spherical or deformed nuclear shapes, the shell-co
rrection energy Delta (sc) steadily washes out with temperature. However, f
or states pertaining to the self-consistent thermally evolving shapes of de
formed nuclei, the dual role played by the single-particle occupancies in d
iluting the fluctuation affects from the single-particle spectra and in dri
ving the system towards a smaller deformation is crucial in determining Del
ta (sc) at moderate temperatures. In rare-earth nuclei, it is found that De
lta (sc) builds up strongly around the shape transition temperature; for li
ghter deformed nuclei like Zn-64 and Zn-66, this is relatively less promine
nt.