We studied the thermal evolution of the central region of a $0.9 \, M_ C/O white dwarf at the initial stage of ion mixture crystallization by numerically solving the heat equation on a fine spatial and temporal grid and by including a detailed treatment of the latent heat release. The formation of two spherical shells is observed. The outer one surrounds a region where crystallization has begun. The inner one bounds a fully solidified core that has exhausted its latent heat. The region between the shells is partially liquid and partially solid. It gradually emits the latent heat generated by crystallization and also releases light elements (carbon) in the process of element redistribution, which accompanies the mixture solidification. Assuming that all released light elements cross the outer shell, we estimated the flux induced by the mixture crystallization. The resulting flux is not divergent and is much lower than the estimate derived from the growth rate of the fully crystallized core.