  Based on a newly derived microscopic fractional quantum Hall edge model, we
study its thermodynamics at finite temperature. For the dressed energy spectrum
a critical energy scale determined by the temperature exists, below which the
refractive dispersion which is essential to the model's bosonization to a
Luttinger liquid is smeared. According to this observation, a
temperature-dependent crossover picture is proposed, and applied to the
analysis of a recent tunneling experiment in comparison with the standard
Luttinger liquid theory, and a better fit to the features of the measured
conductance-temperature curve is achieved. We also consider the role of the
Coulomb interaction in the thermodynamics and find that a crossover exists
during which the influence of the Coulomb interaction is suppressed with the
increase of temperature.
