During the curing process of composite parts manufactured by resin transfer molding (RTM), the volume loss of the resin while polymerizing (chemical shrinkage) and its thermal contraction while cooling the part at the end of the cure cycle, have a major impact on the pressure in the mold and on the formation of residual stresses in the part. A pressure drop when the resin is not fully cured yet may lead to void formation; residual stresses may affect damage and the final shape of the part. The stress evolution is influenced by the viscoelastic behavior of the resin, which is modeled by a temperature and cure dependent generalized Maxwell model. The viscoelastic behavior of the composite material is obtained by homogenization using the Laplace-Carson transform. Due to creep and relaxation effects in the resin, the coefficient of chemical shrinkage (CCS) and the coefficient of thermal expansion (CTE) of the composite are time-dependent. This is taken into account using an analogous approach as for the time-dependence of the viscoelastic behavior. When applying the Laplace-Carson transform to the viscoelastic behavior with the time-dependent CCS and CTE, a classical thermo-elastic form is obtained. The viscoelastic behavior and the expansion coefficients are thus homogenized in the transformed space by standard thermo-elastic homogenization methods. The homogenized behavior of the composite in the time domain is obtained by solving the inverse Laplace-Carson transform by a least-squares problem with Tikhonov regularization. This method naturally yields time-dependent expansion coefficients for a composite whose constituent materials have time-independent expansion coefficients, but a time-dependent viscoelastic behavior. The homogenized behavior is used to simulate the curing process of a composite plate with a 3D woven reinforcement. Two scale changes are needed to first obtain the homogenized behavior of the tows and then the behavior of the composite. The injection pressure of the resin is taken into account by an additional parametric strain with the same formulation as for the CCS. It simulates the effect of the resin added during the curing process on the composite strain. This thermo-mechanical simulation takes as input parameters the local temperature and cure evolution obtained with a thermo-kinetic simulation of the curing process, taking into account reaction heat generation and transient thermal effects.