Thermoset polymers are examples of chemically cured, network-forming materials whose bulk properties depend sensitively on formulation chemistry and reaction conditions. In this work, we employ molecular dynamics simulations to model polyester-based urethane thermosets that are specifically targeted for coating applications. Parameterizing force field interactions with a statistical associating fluid theory (SAFT)-gamma Mie approach in conjunction with corresponding state correlations [Mejia, A; et al. Ind. Eng. Chem. Res. 2014, 53, 4131-4141; Muller, E. A; et al. Langmuir 2017, 33, 11518-11529] permits the facile development of effective models for our thermosetting system. We have devised a theoretical model to fit experimental kinetic data and implement a crosslinking algorithm that replicates the theoretical kinetics. Our molecular simulations capture the cure kinetics regarding the reactions of the isocyanate group with the primary and secondary hydroxyl termini. Analysis of molecular-level connections that arise during crosslinking affords new information about network structure development. Predicted glass transition temperatures and thermomechanical properties agree well with experimental data.