  We consider classical superstring theories on flat four dimensional
space-times, and where N=4 or N=2 supersymmetry is spontaneously broken. We
obtain the thermal and quantum corrections at the string one-loop level and
show that the back-reaction on the space-time metric induces a cosmological
evolution. We concentrate on heterotic string models obtained by
compactification on a T^6 torus and on T^6/Z_2 orbifolds. The temperature T and
the supersymmetry breaking scale M are generated via the Scherk-Schwarz
mechanism on the Euclidean time cycle and on an internal spatial cycle
respectively. The effective field theory corresponds to a no-scale
supergravity, where the corresponding no-scale modulus controls the
Susy-breaking scale. The classical flatness of this modulus is lifted by an
effective thermal potential, given by the free energy. The gravitational field
equations admit solutions where M, T and the inverse scale factor 1/a of the
universe remain proportional. In particular the ratio M/T is fixed during the
time evolution. The induced cosmology is governed by a Friedmann-Hubble
equation involving an effective radiation term ~1/a^4 and an effective
curvature term ~1/a^2, whose coefficients are functions of the complex
structure ratio M/T.
