What happens to energy to during the formation of a soulotion

The main reason is the establishment of the steady state regime where the heat lost to the environment is compensating the heat injected to the system at the interface between the melt and the growing crystallites. At the very early stage of the crystallization process the transient regime dominates or appears which shows the local temperature variations more or less at the vicinity of the interface separating melt and solid phases. But this has very short duration depending upon the cooling rate, which is most control by the surrounding temperature (mold walls) and the heat conductivity of the growing crystal.