  In this paper, we investigate thermal equilibrium in string gas cosmology
which is dominated by closed string.We consider two interesting regimes,
Hagedorn and radiation regimes.We find that for short strings in small radius
of Hagedorn regime very large amount of energy requested to have thermal
equilibrium but for long strings in such system a few energy is sufficient to
have thermal equilibrium. On the other hand in the large radius of Hagedorn
regime, which pressure is not negligible, we obtain a relation between the
energy and pressure in terms of cosmic time which is satisfied by thermal
equilibrium. Then we discuss about radiation regime and find that in all cases
there is thermal equilibrium.
