  We study the temperature structure of the naive TAP equations by mean of a
recursion algorithm. The problem of the chaos in temperature is addressed using
the notion of the temperature evolution of equilibrium states. The lowest free
energy states show relevant correlations with the ground state, and a careful
finite size analysis indicates that these correlations are not finite size
effects, ruling out the possibility of chaos in temperature even in the
thermodynamic limit. The correlations of the equilibrium states with respect to
the ground state are investigated. The performance of a new heuristic algorithm
for the search of ground states is also discussed.
