The work focuses on the calculation of the effective properties of non-aging linear viscoelastic and hierarchical composite materials, reinforced by wavy fibers in two directions. In particular, we investigate the effects that two different temperatures of a polymeric matrix, and the waviness of transversely isotropic fibers made from a carbon nanotube-reinforced polymer, have on the macroscopic viscoelastic behavior of a hierarchical structure. For this purpose, we consider the elasticviscoelastic correspondence principle and the Laplace-Carson transform, and we apply the three-scale asymptotic homogenization method (AHM). The expressions for the associated local and homogenized problems, and the effective coefficients are derived at each level of organization. We solve the meso and microscale local problems in Laplace-Carson domain, by means of an analytically approach and finite element three-dimensional simulations, respectively. We obtain the effective creep and relaxation behavior of the composite. In addition, we use a numerical algorithm to invert the Laplace-Carson transform and derive the properties in the time domain. Finally, we present the results of our computations. They confirm that temperature and waviness can affect the macroscopic behavior of the hierarchical heterogeneous structure.