The entropy balance associated with a Budyko‐Sellers climatic model is developed. It is shown that different regimes, associated with decreasing, as well as increasing values of entropy production (which measures the rate of dissipation in the system) in the course of time are possible. This immediately poses the problem of stability of steady states of the climatic system. An explicit criterion of climatic stability is thus derived, which is expressed in terms of thermodynamic quantities related to excess entropy production. The results are illustrated on simple cases involving diffusive energy transport. A comparison with Paltridge's minimum entropy exchange principle is also attempted.