  Effects of thermal conductivity on the dynamics of first-order phase
transitions are studied. Important consequences of a difference of the
isothermal and adiabatic spinodal regions are discussed. We demonstrate that in
hydrodynamical calculations at non-zero thermal conductivity, $\kappa \neq 0$,
onset of the spinodal instability occurs, when the system trajectory crosses
the isothermal spinodal line. Only for $\kappa = 0$ it occurs at a cross of the
adiabatic spinodal line. Therefore ideal hydrodynamics is not suited for an
appropriate description of first-order phase transitions.
