The standard inflationary hot Big Bang model of cosmology has long been known to suffer from moduli and gravitino problems. In this talk I describe a Minimal Supersymmetric Cosmological Model, whose particle physics has long been motivated by neutrino masses, an origin for the mu-parameter and the axion solution to the strong CP-problem, and show how it gives rise to a cosmology of thermal inflation, baryogenesis and axino/axion dark matter, providing a consistent history for the middle ages of the universe between primordial inflation and Big Bang nucleosynthesis.