  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.
