  We consider the non-relativistic Hartree model in the gravitational case,
i.e. with attractive Coulomb-Newton interaction. For a given mass, we construct
stationary states with non-zero temperature by minimizing the corresponding
free energy functional. It is proved that minimizers exist if and only if the
temperature of the system is below a certain threshold(possibly infinite),
which itself depends on the specific choice of the entropy functional. We also
investigate whether the corresponding minimizers are mixed or pure quantum
states and characterize a positive critical temperature above which mixed
states appear.
