What is Ellingham approximation?

The Ellingham approximation treats $\Delta_r H^\circ$ and $\Delta_r S^\circ$ as independent of the temperature over an interval containing no change of state. Then $\Delta_r G^\circ(T) = \Delta_r H^\circ - T\Delta_r S^\circ$ is a straight line in $T$, of slope $-\Delta_r S^\circ$.