We are interested in characterizing the linear viscoelasticity of unidirectional (UD) composites which are transversely isotropic. The materials of interest are long carbon fibers randomly distributed in the transverse plane and embedded in a thermoplastic polymer matrix. Their application as hydrogen tanks require an estimation of their viscoelasticity in order to evaluate some possible creep. Unfortunately, the linear viscoelasticity of anisotropic materials is difficult to characterize experimentally. Classic dynamic torsional or bending tests available in laboratories do not provide access to each of the five parameters of the transverse isotropic behavior independently. Thanks to simple finite element simulations, we will show that experimental measures from torsional tests are the result of a complex coupling between those five parameters. Therefore, micromechanics modeling has been used to predict the effective behavior of the composites. Because of the linear nature of the considered behavior, we have performed FFT-based homogenization calculations in the frequency domain considering microstructures with random or regular hexagonal distributions of fibers. The isotropic linear viscoelasticity of the matrix has been characterized experimentally. The elasticity of carbon fibers is only partially known, hence two cases have been considered : isotropic and transversely isotropic fibers. We have estimated the storage and loss moduli of the composites by characterizing their viscoelastic behavior using dynamic loading at 1 Hz and various temperatures, from the glassy state to the rubbery state of the polymer matrix. Our results compare the results of the FFT calculations on both random and hexagonal distributions of fibers to the mean-field model from Christensen and Lo which has already shown to predict well some numerical results. We show that as long as either the contrast in behavior between the matrix and the fibers or the volume fraction of fibers are not too high, the hexagonal and the random microstructures provide similar results that are well estimated by the mean-field model. However, when the contrast between the phases increases (i.e. when the matrix is in the rubbery state) or when the amount of fillers increases above 45% (which is very common for those materials), the mean-field model fails to reproduce the results of the FFT calculations.