The effect of aeration on the thermal stability of a self-heating powder bed is mathematically discussed. Judging from the thermal characteristics in the steady state, aeration greatly improves the thermal stability. It is also shown, however, that a steady state solution for the temperature distribution in the bed always accompanies an unstable equilibrium solution. It follows that once the steady state temperature distribution is forced through the unstable one by some external disturbances, the powder bed starts to run away towards an ignition and loses stability even after the disturbances are removed. An aerated powder bed is rather susceptible to this kind of ignition. To avoid possible risk of such an ignition, a restorable limit of the temperature distribution for a given aerated powder bed is proposed. Aeration should be controlled so that the temperature at any position in the powder bed is kept well below the restorable limit distribution.