  We consider four dimensional heterotic string backgrounds for which
supersymmetry is spontaneously broken via the Scherk-Schwarz mechanism on an
internal spatial cycle and by finite temperature effects. We concentrate on
initially flat backgrounds with N=4 and N=2 amount of supersymmetry. Thermal
and quantum corrections give rise to a non-trivial cosmological evolution. We
show that these corrections are under control and calculable due to the
underlying no-scale structure of the effective supergravity theory. The
effective Friedmann-Hubble equation involves a radiation term ~1/a^4 and a
curvature term ~1/a^2, whose coefficients are functions of ratio of the
gravitino mass scale to the temperature.
