  The existence of non-singular string cosmologies is established in a class of
two-dimensional supersymmetric Hybrid models at finite temperature. The
left-moving sector of the Hybrid models gives rise to 16 real (N_4=4) spacetime
supercharges as in the usual superstring models. The right-moving sector is
non-supersymmetric at the massless level, but is characterized by MSDS
symmetry, which ensures boson/fermion degeneracy of the right-moving massive
levels. Finite temperature configurations, which are free of Hagedorn
instabilities, are constructed in the presence of non-trivial
"gravito-magnetic" fluxes. These fluxes inject non-trivial winding charge into
the thermal vacuum and restore the thermal T-duality symmetry associated with
the Euclidean time circle. Thanks to the unbroken right-moving MSDS symmetry,
the one-loop string partition function is exactly calculable beyond any
alpha'-approximation. At the self-dual point new massless thermal states
appear, sourcing localized spacelike branes, which can be used to connect a
contracting thermal Universe to an expanding one. The resulting bouncing
cosmology is free of any curvature singularities and the string coupling
remains perturbative throughout the cosmological evolution.
