A dynamic multiscale micromechanics model that accounts for two-way thermomechanical coupling in composites is presented. It predicts not only the standard deformation that results from a temperature change, but also the temperature change that results from mechanical deformation. In addition, viscoplastic material behavior is included at the scale of the fiber/matrix constituents in a local High-Fidelity Generalized Method of Cells analysis, which is conducted at each material point of a global analysis on a composite specimen. The global analysis of the composite considers time-dependent thermomechanical boundary conditions capable of simulating impact loading while solving the coupled transient thermal problem and the dynamic mechanical problem. Effective thermoelastic and physical properties, as well as homogenized inelastic strains are provided to the global model from the local scale. The multiscale model was employed to examine the impact response of carbon/epoxy and SiC/Ti composites with emphasis on the temperature changes and inelastic strains induced by the impact loading. It was found that the behavior of the two types of composites was quite different, with the differences traceable to the effect of the matrix material properties on the terms within the energy equation, which governs the heat generation.