  The irreversible growth of thin films under far-from-equilibrium conditions
is studied in $(2+1)-$dimensional strip geometries. Across one of the
transverse directions, a temperature gradient is applied by thermal baths at
fixed temperatures between $T_1$ and $T_2$, where $T_1<T_c^{hom}<T_2$ and
$T_c^{hom}=0.69(1)$ is the critical temperature of the system in contact with
an homogeneous thermal bath. By using standard finite-size scaling methods, we
characterized a continuous order-disorder phase transition driven by the
thermal bath gradient with critical temperature $T_c=0.84(2)$ and critical
exponents $\nu=1.53(6)$, $\gamma=2.54(11)$, and $\beta=0.26(8)$, which belong
to a different universality class from that of films grown in an homogeneous
bath. Furthermore, the effects of the temperature gradient are analyzed by
means of a bond model that captures the growth dynamics. The interplay of
geometry and thermal bath asymmetries leads to growth bond flux asymmetries and
the onset of transverse ordering effects that explain qualitatively the shift
in the critical temperature.
