The mathematical model, describing a movement of emulsion under the specified conditions, was formulated by O.V. Voinov and V.V. Pukhnachev [1]. One-dimensional model of the process of solidification of emulsion, moving under the action of thermocapillary forces and microgravitation with small concentration of disperse phase was given by A.G. Petrova and V.V. Pukhnachev [2]. In the given paper the opportunity of obtaining the given concentration distribution of disperse in solidified matrix with operating the temperature on the solid boundary is considered. The solvability of a problem for the case of self-similar mode of solidification is proved.