We simulate the phase-separation dynamics under a temperature gradient by solving numerically the coupled Langevin equations of a “fluid model” (model H) and a Fourier’s equation. It is found that the macroscopically phase-separated structure is formed in the case that the one side of the system is hotter than phase separation temperatureTcand the another side is cooler thanTc.In the simulation without velocity field, on the other hand, the coexistence of the mixing and demixing states is observed, reflecting the local temperature. This clearly indicates that the velocity fields play a crucial role in the phase-separation behavior in such a non-equilibrium condition. ©2000 American Institute of Physics.