This article concerns the minimization of residual thermal stresses in geometrically constrained adhesive layers and thin polymeric composite lay-ups with emphasis on the role of initial stresses. Such residual stresses evolve during cure and subsequently during post-cure cool-down. The cure stresses play the role of initial stress superimposed on the thermoviscoelastic response that governs to cool-down phase. Optimization is achieved by following a time-temperature path that achieves the best counter play between temperature as a stress inducing and a stress reducing agent. When viscoelastic nonlinearity is considered such contradictory effect is played by stress itself, in which case an initial stress may have a beneficial effect.