  We study the transient response of an electrolytic cell subject to a small,
suddenly applied temperature increase at one of its two bounding electrode
surfaces. An inhomogeneous temperature profile then develops, causing, via the
Soret effect, ionic rearrangements towards a state of polarized ionic charge
density $q$ and local salt density $c$. For the case of equal cationic and
anionic diffusivities, we derive analytical approximations to $q, c$, and the
thermovoltage $V_{T}$ for early ($t\ll\tau_{T}$) and late ($t\gg\tau_{T}$)
times as compared to the relaxation time $\tau_{T}$ of the temperature. We
challenge the conventional wisdom that the typically large Lewis number, the
ratio $a/D$ of thermal to ionic diffusivities, of most liquids implies a
quickly reached steady-state temperature profile onto which ions relax slowly.
Though true for the evolution of $c$, it turns out that $q$ (and $V_{T}$) can
respond much faster. Particularly when the cell is much bigger than the Debye
length, a significant portion of the transient response of the cell falls in
the $t\ll\tau_{T}$ regime, for which our approximated $q$ (corroborated by
numerics) exhibits a density wave that has not been discussed before in this
context. For electrolytes with unequal ionic diffusivities, $V_{T}$ exhibits a
two-step relaxation process, in agreement with experimental data of Bonetti et
al. [J. Chem. Phys. 142, 244708 (2015)].
