  We study the hadron-quark phase transition with the finite size effects at
finite temperature. For the hadron phase, we adopt a realistic equation of
state in the framework of the Brueckner-Hartree-Fock theory including hyperons.
The properties of the mixed phase are clarified by considering the finite size
effects under the Gibbs conditions. We find that the equation of state becomes
softer than that at zero-temperature for some density region. We also find that
the equation of state gets closer to that given by the Maxwell construction.
Moreover, the number of hyperons is suppressed by the presence of quarks. These
are characteristic features of the hadron-quark mixed phase, and should be
important for many astrophysical phenomena such as mergers of binary neutron
stars.
