I would like to do some calculations for the evolution of the temperature of the universe with a homogeneous distribution of light sources in some simple models. For example, starting with the simplest one, consider a universe with an origin of time and with a static space. The integral of the bolometric flux received from different shells from r = 0 up to r = c T (T the age of the universe) is finite and there is no Olbers' paradox. However, such a model "tends" to a paradox as T -> infinity with a diverging flux integral. Consider an object which is created at the same time than the universe (t = 0). How can be calculated the time (or time scale) for this body to reach nearly thermal equilibrium with the radiation emitted by the light sources (and on what does this depend)? Let's call this time T_eq. Consider now a body created (or "inserted in this universe") at t > T_eq. How long does it take for this body to reach thermal equilibrium?