  The agreement between the fragments' internal and kinetic temperatures with
the breakup temperature is investigated using a Statistical Multifragmentation
Model which makes no a priori as- sumption on the relationship between them. We
thus examine the conditions for obtaining such agreement and find that, in the
framework of our model, this holds only in a relatively narrow range of
excitation energy. The role played by the qualitative shape of the fragments'
state densities is also examined. Our results suggest that the internal
temperature of the light fragments may be affected by this quantity, whose
behavior may lead to constant internal temperatures over a wide excitation
energy range. It thus suggests that the nuclear thermometry may provide
valuable information on the nuclear state density.
