The number of steady solutions of the heat equation is determined for given control parameters in axisymmetric or ergodic divertors. Several impurity species are used (C,O,Fe) with coronal or non-coronal assumptions. The authors show that the number of equilibria strongly depends on the radiation emission and on the boundary conditions at the wall. A strong concentration of light impurity is needed for several thermal equilibria to exist and bifurcation to be possible.