An analytic two-zone model for the advance of a crystallization front through a porous amorphous ice medium is proposed. Such a model is justified by the extremely low thermal conductivity of cold amorphous ice on the one hand, and by the very high thermal conductivity of vapor-filled porous crystalline ice on the other hand. Steady state solutions are sought, where the only energy source is the heat released upon crystallization. Part of this energy is used in sublimation of the ice at the free boundary of the crystalline layer, and part is used in heating of the amorphous ice that sustains the crystallization process. It is shown that this process is capable of maintaining quite high temperatures throughout the crystalline layer behind the phase-transition front. These result in high rates of sublimation