  We study string-gas cosmology in dilaton gravity, inspired by the fact that
it naturally arises in a string theory context. Our main interest is the
thermodynamical treatment of the string-gas and the resulting implications for
the cosmology. Within an adiabatic approximation, thermodynamical equilibrium
and a small, toroidal universe as initial conditions, we numerically solve the
corresponding equations of motions in two different regimes describing the
string-gas thermodynamics: (i) the Hagedorn regime, with a single scale factor,
and (ii) an almost-radiation dominated regime, which includes the leading
corrections due to the lightest Kaluza Klein and winding modes, with two scale
factors. The scale factor in the Hagedorn regime exhibits very slow time
evolution with nearly constant energy and negligible pressure. By contrast, in
case (ii) we find interesting cosmological solutions where the large dimensions
continue to expand and the small ones are kept undetectably small.
