The thermodiffusive behavior of a Lennard-Jones binary mixture has been studied by using nonequilibrium molecular dynamics. In particular, the dependence of the Soret coefficient, S(T), on the temperature and composition has been investigated, exploring a wide range of temperatures from 1000 K to the condensation temperature of the mixture. In a previous paper the dependence of S(T) on the temperature and the composition was studied for Lennard-Jones binary mixtures presenting mixing/demixing (consolute) phase transition, and the results allowed the formulation of a very simple expression with the computed values of S(T) in the one phase region outside the critical region closely fitted by the function [T - T(c)(x(1))](-1), with T(c)(x(1)) the demixing temperature of the mixture under study. The results of the present work show that the same expression of S(T) can be found for the one phase region outside the evaporation/condensation region but now with T(c) representing the condensation temperature of the mixture under study.