  The dependence of fission barriers on the excitation energy of the compound
nucleus impacts the survival probability of superheavy nuclei synthesized in
heavy-ion fusion reactions. In this work, we investigate the isentropic fission
barriers by means of the self-consistent nuclear density functional theory. The
relationship between isothermal and isentropic descriptions is demonstrated.
Calculations have been carried out for $^{264}$Fm, $^{272}$Ds, $^{278}$112,
$^{292}$114, and $^{312}$124. For nuclei around $^{278}$112 produced in "cold
fusion" reactions, we predict a more rapid decrease of fission barriers with
excitation energy as compared to the nuclei around $^{292}$114 synthesized in
"hot fusion" experiments. This is explained in terms of the difference between
the ground-state and saddle-point temperatures. The effect of the particle gas
is found to be negligible in the range of temperatures studied.
