  We investigate the high-temperature effect on the nuclear matter that
consists of mixture of nucleons and all nuclei in the dense and hot stellar
environment. The individual nuclei are described within the compressible
liquid-drop model that is based on Skyrme interactions for bulk energies and
that takes into account modifications of the surface and Coulomb energies at
finite temperatures and densities. The free-energy density is minimized with
respect to the individual equilibrium densities of all heavy nuclei and the
nuclear composition. We find that their optimized equilibrium densities become
smaller and smaller at high temperatures because of the increase of thermal
contributions to bulk free energies and the reduction of surface energies. The
neutron-rich nuclei become unstable and disappear one after another at some
temperatures. The calculations are performed for two sets of model parameters
leading to different values of the slope parameter in the nuclear symmetry
energy. It is found that the larger slope parameter reduces the equilibrium
densities and the melting temperatures. We also compare the new model with some
other approaches and find that the mass fractions of heavy nuclei in the
previous calculations that omit vaporization are underestimated at $T \lesssim
10$MeV and overestimated at $T\gtrsim10$~MeV. The further sophistication of
calculations of nuclear vaporization and of light clusters would be required to
construct the equation of state for explosive astrophysical phenomena.
