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 to 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. (C) 1997 Elsevier Science B.V.