A new type of instability is shown to occur if a temperature gradient is present across a $n{n}^{+}$, $p{p}^{+}$, or $pn$ junction with no voltage applied. The critical temperature gradient depends on the size and steepness of the junction and is smaller for large and less abrupt junctions. The instability should occur in the best thermoelectric materials, characterized by a figure of merit $ZTg1$. In other materials the required temperature difference between the homogeneous semiconductors at the end of the junction turns out to be too large.