  A systematic study of fission-barrier dependence on excitation energy has
been performed using the self-consistent finite-temperature Hartree-Fock+BCS
(FT-HF+BCS) formalism with the SkM* Skyrme energy density functional. The
calculations have been carried out for even-even superheavy nuclei with Z
ranging between 110 and 124. For an accurate description of fission pathways,
the effects of triaxial and reflection-asymmetric degrees of freedom have been
fully incorporated. Our survey demonstrates that the dependence of isentropic
fission barriers on excitation energy changes rapidly with particle number,
pointing to the importance of shell effects even at large excitation energies
characteristic of compound nuclei. The fastest decrease of fission barriers
with excitation energy is predicted for deformed nuclei around N=164 and
spherical nuclei around N=184 that are strongly stabilized by ground-state
shell effects. For nuclei 240Pu and 256Fm, which exhibit asymmetric spontaneous
fission, our calculations predict a transition to symmetric fission at high
excitation energies due to the thermal quenching of static reflection
asymmetric deformations.
