  We investigate the possibility that the Peccei-Quinn phase transition occurs
at a temperature far below the symmetry breaking scale. Low phase transition
temperatures are typical in supersymmetric theories, where symmetry breaking
fields have small masses. We find that QCD axions are abundantly produced just
after the phase transition. The observed dark matter abundance is reproduced
even if the decay constant is much lower than $10^{11}$ GeV. The produced
axions tend to be warm. For some range of the decay constant, the effect of the
predicted warmness on structure formation can be confirmed by future
observations of 21 cm lines. A portion of parameter space requires a mixing
between the Peccei-Quinn symmetry breaking field and the Standard Model Higgs,
and predicts an observable rate of rare Kaon decays.
