# Do we cool the solution to form a precipitate because of lower melting points?

If we have two compounds in aqueous solution, in order to separate one from the other the solution is placed into an ice bath. For example the formation of $$\ce{KClO3}$$ from a combination of $$\ce{NaClO3(aq)}$$ and $$\ce{KCl(aq)}$$.

I am trying to understand why potassium chlorate precipitates out of solution first as the temperature is lowered. My hypothesis is that the melting points for potassium chlorate, which is $$\pu{356 ^\circ C}$$, is lower than that of sodium chloride, which is $$\pu{801 ^\circ C}$$.