The eventual cooling of post-shock gas before the temperature returns to its unperturbed value is studied in a model for a stationary shock in the atmosphere of a Mira Ceti variable star. The cooling time of the gas as a function of the current temperature is calculated. The cooling time is compared to the period of the brightness variations of Mira variables, for which the phase dependence of emission-line intensities is known. In most cases, the gas does not have time to cool to the temperature of the “photosphere”—the region where the molecular absorption bands are formed. Therefore, the shock propagates in subphotospheric layers. This is confirmed by previously published high-resolution spectra, which show absorption lines of molecules superimposed on emission lines.