  Current-driven insulator-metal transitions are in many cases driven by Joule
heating proportional to the square of the applied current. Recent nano-imaging
experiments in Ca$_2$RuO$_4$ reveal a metal-insulator phase boundary that
depends on the direction of an applied current, suggesting an important
non-heating effect. Motivated by these results, we study the effects of an
electric current in a system containing interfaces between metallic and
insulating phases. Derivation of a heat balance equation from general
macroscopic Onsager transport theory, reveals a heating term proportional to
the product of the current across the interface and the discontinuity in the
Seebeck coefficient, so that heat can either be generated or removed at an
interface, depending on the direction of the current relative to the change in
material properties. For parameters appropriate to Ca$_2$RuO$_4$, this heating
can be comparable to or larger than Joule heating. A simplified model of the
relevant experimental geometry is shown to provide results consistent with the
experiments. Extension of the results to other inhomogeneous metal-insulator
transition systems is discussed.
