  We have examined the dependence of the shell correction to the nuclear liquid
drop energy at finite excitations on the excitation energy (temperature). For
this we have calculated the shell correction to the energy and free energy in
very broad region of nuclei and deformations starting directly from their
formal definitions. We have found out that the dependence of the shell
corrections on the excitation energy differ substantially from the widely used
approximation $\delta E(E^*)=\delta E(0)\exp(-E^*/E_d)$ both at small and large
excitations. In particular, below the critical temperature at which the pairing
effects vanish, the shell correction to the free energy is rather insensitive
to the excitation energy.
  We suggest a more accurate approximation for the temperature dependence of
the shell correction to the energy and free energy that is expressed in terms
of the shell correction to the energy of independent particles and the shell
correction to the pairing energy at T=0 and few fitted constants.
