Significant local temperature rises often accompany the high rate deformation of polymer matrix composites. In the case of impact loading, heat is generated locally within the polymer matrix due to plastic dissipation, but the rapid nature of the loading precludes significant heat transfer from occurring; ballistic impact loading can therefore be regarded as fully adiabatic. In this paper, the development of a synergistic multiscale approach to simulate the architecturally dependent impact response of polymer matrix composites with complex fiber tow architectures is presented and applied to a representative triaxially braided composite material system. To approximate the heterogeneity of the composite braid architecture at the highest analysis length scale, a subcell-based approach is utilized whereby the mesoscale repeating unit cell of the material is discretized in-plane into an assemblage of laminated composite subcell regions, with stacking sequences determined from the braid architecture. Each unidirectional layer of the laminated composite subcells are modeled with the generalized method of cells micromechanics theory, where a nonisothermal viscoplastic constitutive model is employed to model the rate, temperature, and pressure dependent polymer matrix. Matrix temperature rises due to inelastic deformation are computed at the microscale, assuming adiabatic conditions. Temperature and rate dependent shifts in matrix elastic properties are determined from neat resin dynamic mechanical analysis data. The commercial transient dynamic finite element code LS-DYNA is utilized to conduct simulations of quasi-static coupon tests and flat panel impact tests performed on a T700/PR520 [0°/60°/-60°] triaxially braided composite. Good agreement is found between simulations and experiments. It is expected that, once progressive damage and failure are incorporated into the multiscale scheme, the incorporation of adiabatic heating affects will greatly improve the predictive capability of current models.