  We apply the second-order Israel-Stewart theory of relativistic fluid- and
thermodynamics to a physically realistic model of a radiative fluid in a simple
anisotropic cosmological background. We investigate the asymptotic future of
the resulting cosmological model and review the role of the dissipative
phenomena in the early Universe. We demonstrate that the transport properties
of the fluid alone, if described appropriately, do not explain the presently
observed accelerated expansion of the Universe. Also, we show that, in
constrast to the mathematical fluid models widely used before, the radiative
fluid does approach local thermal equilibrium at late times, although very
slowly, due to the cosmological expansion.
