Directed self-assembly of block copolymers has shown to be an effective bottom-up approach to creating periodic nanoscale surface patterns. This work offers a computational study of sphere-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) block copolymer thin-film behavior. A temperature-dependent-optimized phase-field model is implemented for simulations. Directed self-assembly using a combination of cold-zone annealing and chemoepitaxial templating is performed. It is shown that synergy between these methods can enhance long-range order within the evolving system during microphase separation and that templated patterns can propagate indefinitely into untemplated regions when the system undergoes low-velocity cold-zone annealing.