The viscosity and the thermal conductivity of slag are among two of the most important material properties that need to be studied. In this paper we review the existing theoretical and experimental correlations for the thermal conductivity of slag. However, since, in general, slag behaves as a non-linear fluid, it is the heat flux vector which must be studied. Both explicit and implicit approaches are discussed and suggestions about the form of the heat flux vector and the thermal conductivity and their dependence on shear rate, porosity, deformation, etc. are provided. The discussion of the constitutive modeling of the heat flux vector for slag is from a theoretical perspective.