  We study the thermodynamics of Na_8 and Na_{20} clusters using
multiple-histogram methods and an ab initio treatment of the valence electrons
within density functional theory. We consider the influence of various electron
kinetic-energy functionals and pseudopotentials on the canonical ionic specific
heats. The results for all models we consider show qualitative similarities,
but also significant temperature shifts from model to model of peaks and other
features in the specific-heat curves. The use of phenomenological
pseudopotentials shifts the melting peak substantially (~ 50--100 K) when
compared to ab-initio results. It is argued that the choice of a good
pseudopotential and use of better electronic kinetic-energy functionals has the
potential for performing large time scale and large sized thermodynamical
simulations on clusters.
