  We study the cosmology of perturbative heterotic superstring theory during
the radiation-like era for semi-realistic backgrounds with initial $\N=1$
supersymmetry. This analysis is valid for times after the Hagedorn era (or
alternatively inflation era) but before the electroweak symmetry breaking
transition. We find an attraction to a radiation-like era with the ratio of the
supersymmetry breaking scale to temperature stabilized. This provides a
dynamical mechanism for setting the supersymmetry breaking scale and its
corresponding hierarchy with the Planck scale. For the internal space, we find
that orbifold directions never decompactify, while toroidal directions may
decompactify only when they are wrapped by certain geometrical fluxes which
break supersymmetry. This suggests a mechanism for generating spatial
directions during the radiation-like era. Moreover, we show that certain moduli
may be stabilized during the radiation-like era with masses near the
supersymmetry breaking scale. In addition, the moduli do not dominate at late
times, thus avoiding the cosmological moduli problem.
