Residual stress development in heterogeneous or composite materials is an important problem in manufacture process modeling. Composites possess an intricate microstructure in which the mismatch in thermal expansion coefficients between the fiber and matrix can lead to residual thermal stresses upon part cool-down. It is commonly assumed that prior to cool-down, the entire composite at both micro and macro length scales is at a zero stress temperature. As cool-down initiates, the mismatch in thermostress behavior and the mismatch in viscoelastic time-dependent behavior of the two phases lead to built-in residual stresses in the final product. A novel finite element approach is presented here for the coupled thermovisoelastic analysis of polymer-matrix composite structures containing microscopic heterogeneities. Due to its inherent advantages over other techniques, the asymptotic homogenization approach is employed to obtain the homogenized properties for use in the macroscale problem. For illustration, a simple Kelvin-Voight viscoelastic solid is studied to demonstrate the formulations involved in similar materials for which the time-dependent stress-strain relationship is subsequently homogenized. The formulation accounts for the dissipative corrector behavior for heterogeneous viscoelastic materials. An analytical solution for the degenerative homogeneous viscoelastic material subject to uniform thermal relaxation is employed to verify part of the formulations. Additional examples are shown to further illustrate the approach for more complex scenarios.