The method of separating a mixture of soluble solids by dissolving them in a suitable hot solvent and then lowering the temperature slowly is called:

Explanation

Fractional crystallisation separates soluble solids using differences in their solubilities and how those solubilities change with temperature. A hot solution is cooled so that components crystallise in different fractions. Sublimation uses a solid-to-gas change, while the distillation alternatives concern separation through vapour formation and condensation.