  We study cosmological implications of supersymmetric axion models in which
the axion scale is generated radiatively. Such models lead to the so-called
thermal inflation and subsequent reheating should be constrained not to yield a
too large axion energy density at the time of nucleosynthesis. We examine how
plausible it is that this nucleosynthesis constraint is satisfied for both
hadronic and Dine-Fischler-Srednicki-Zhitnitskii type axion models.
Baryogenesis and the possibility for raising up the cosmological upper bound on
the axion scale in thermal inflation scenario are also discussed.
