Summary: Self-dual string cosmological models provide an effective example of bouncing solutions where a phase of accelerated contraction smoothly evolves into an epoch of decelerated Friedmann-Robertson-Walker expansion dominated by the dilaton. While the transition to the expanding regime occurs at sub-Planckian curvature scales, the universe emerging after the bounce is cold, with sharply growing gauge coupling. However, since massless gauge bosons (as well as other massless fields) are super-adiabatically amplified, the energy density of the maximally amplified modes re-entering the horizon after the bounce can efficiently heat the universe. As a consequence the gauge coupling reaches a constant value, which can still be perturbative.