  Within an adiabatic approximation, thermodynamical equilibrium and a small,
nine dimensional, toroidal universe as initial conditions, we analyze the
evolution of the dimensions in two different regimes: (i) the Hagedorn regime,
with a single scale factor with a nearly constant time evolution (ii) an
almost-radiation dominated regime, including the leading corrections due to the
lightest Kaluza Klein and winding modes, in which for some initial conditions
the large dimensions continue to expand and the small ones remain small.
