  We perform Shell Model Monte Carlo calculations to study pair correlations in
the ground states of $N=Z$ nuclei with masses A=48-60. We find that $T=1$,
$J^{\pi}=0^+$ proton-neutron correlations play an important, and even dominant
role, in the ground states of odd-odd $N=Z$ nuclei, in agreement with
experiment. By studying pairing in the ground states of $^{52-58}$Fe, we
observe that the isovector proton-neutron correlations decrease rapidly with
increasing neutron excess. In contrast, both the proton, and trivially the
neutron correlations increase as neutrons are added.
  We also study the thermal properties and the temperature dependence of pair
correlations for $^{50}$Mn and $^{52}$Fe as exemplars of odd-odd and even-even
$N=Z$ nuclei. While for $^{52}$Fe results are similar to those obtained for
other even-even nuclei in this mass range, the properties of $^{50}$Mn at low
temperatures are strongly influenced by isovector neutron-proton pairing. In
coexistence with these isovector pair correlations, our calculations also
indicate an excess of isoscalar proton-neutron pairing over the mean-field
values. The isovector neutron-proton correlations rapidly decrease with
temperatures and vanish for temperatures above $T=700$ keV, while the isovector
correlations among like nucleons persist to higher temperatures. Related to the
quenching of the isovector proton-neutron correlations, the average isospin
decreases from 1, appropriate for the ground state, to 0 as the temperature
increases.
