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 264Fm, 272Ds, ;{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.