Abstract
The exact solutions of the relativistic hyperbolic heat equation on a flat Friedman spacetime metric are obtained. These solutions are obtained in three cases of flat Friedman model which correspond to radiation, matter and dark energy-dominated universe models. In particular, in the dark energy-dominated universe case, a closed form solution is obtained for which, using appropriate boundary conditions, an interesting exact solution is derived. This solution suggests that the temperature of the universe drops as it expands by a scale of an exponential function.