  We perform Shell Model Monte Carlo calculations of selected N=Z pf-shell
nuclei with a schematic hamiltonian containing isovector pairing and
quadrupole-quadrupole interactions. Compared to realistic interactions, this
hamiltonian does not give rise to the SMMC ``sign problem'', while at the same
time resembles essential features of the realistic interactions. We study
pairing correlations in the ground states of N=Z nuclei and investigate the
thermal dependence of selected observables for the odd-odd nucleus Co54 and the
even-even nuclei Zn60 and Ni60. Comparison of the present results to those with
the realistic KB3 interaction indicates a transition with increasing
temperature from a phase of isovector pairing dominance to one where isoscalar
pairing correlations dominate. In addition, our results confirm the qualitative
reliability of the procedure used to cure the sign problem in the SMMC
calculations with realistic forces.
