A numerical model is developed to simulate the phase separation of binary Upper CST mixtures confined between two opposite cooled walls. The modeling is attempted to simulate the heat transfer enhancement obtained experimentally during phase separation of partially miscible solvent mixtures. With a critical composition, the initial homogeneous mixture undergoes spinodal decomposition, when the walls are cooled below the critical temperature. A new formulation is suggested for the typical length scale (a) of the spatial inhomogeneity that is included in the generalized free energy coarse-grained Landau-Ginzburg functional. The new formulation is based on physical considerations and accounts for the temperature variation of this length scale. A careful modeling of this temperature dependency is shown to be important for simulating the phenomena during spinodal decomposition under non-isothermal conditions.