The hypothesis of minimum entropy production is applied to a simple one-dimensional energy balance model and is analysed for different values of the radiative forcing due to greenhouse gases. The extremum principle is used to determine the planetary “conductivity” and to avoid the “diffusive” approximation, which is commonly assumed in this type of model. For present conditions the result at minimum radiative entropy production is similar to that obtained by applying the classical model. Other climatic scenarios show visible differences, with better behaviour for the extremal case