  We investigate in the Hartree Fock approximation the temperature and filling
dependence of the superconducting $\pi$-phase for the Penson-Kolb-Hubbard
model. Due to the presence of the pair-hopping term, the phase survives for
repulsive values of the on-site Coulomb interaction, exhibiting an interesting
filling and temperature dependence. The structure of the self-consistent
equations peculiar to the $\pi$-phase of the model allows to explicitly solve
them for the chemical potential. The phase diagrams are shown and discussed in
dimension 2 and 3. We also show that, when a next-nearest neighbours hopping
term is included, the critical temperature of the superconducting region
increases, and the corresponding range of filling values is shifted away from
half-filling. Comparison with known exact results is also discussed.
