This paper presents the numerical comparison in the solution of the hyperbolic transport Equation that models the heat flux in thermoelectric materials at nanometric length scales when the wave propagation of heat dominates the diffusive transport described by Fourier’s law. The widely used standard finite difference method fails in well-reproducing some of the physics presented in such systems at that length scale level. As an alternative, the spectral methods assure a well representation of wave behavior of heat given their spectral convergence.