  We study the realisation of supersymmetric discrete flavour symmetry models
to the thermal history of our universe. We focus on the evolution of the pseudo
moduli field among the flavons by taking into account finite temperature
corrections. We show that the pseudo moduli flavon dominates the energy density
of our universe and this domination makes crucially difficult to realise the
flavour symmetry models in our universe. We also discuss possible extensions of
the supersymmetric discrete flavour symmetry models which can ensure the
consistency of the models with the thermal history of our universe. Finally, we
show an extension to realise the thermal inflation by the flavon domination.
