A mathematical model and computer simulations are used to describe the dynamics of thermally induced phase separation (TIPS) by spinodal decomposition for polymer blends (single quench and double quench) using the nonlinear Cahn-Hilliard theory and the Flory-Huggins-de Gennes free energy. The importance of TIPS is to enhance material properties such as toughness, impact resistance and elasticity. Therefore, controlling the morphology is a critical factor in optimizing performance. The numerical results for the single quench are consistent with known characteristics of phase separation by spinodal decomposition observed in polymer blends. The numerical results for double quenching replicate recently published experimental and numerical work. Under a double quench the numerical work shows that a critical quench depth exists before secondary phase separation occurs, the growth rate of the primary and secondary structures are dependent on domain size and early stage dynamics for the secondary structures, after the second jump, appears to follow the linear Cahn-Hilliard theory.