A numerical method is proposed for solving ternary nonisothermal multistage extraction problems by the relaxation method. The algorithm was developed by adding a temperature correction loop to the method previously proposed by Liu et al. for isothermal cases. The enthalpy balance for the temperature correction includes heat flows to/from the surroundings and heat of mixing. Although empirical equations are employed for predicting ternary liquid-liquid equilibria, the method can be extended to multicomponent systems by applying other thermodynamic methods. The stability of the proposed method is illustrated by sample calculations.