  We study the hadron-quark phase transition in the interior of protoneutron
stars. For the hadronic sector, we use a microscopic equation of state
involving nucleons and hyperons derived within the finite-temperature
Brueckner-Bethe-Goldstone many-body theory, with realistic two-body and
three-body forces. For the description of quark matter, we employ the MIT bag
model both with a constant and a density-dependent bag parameter. We calculate
the structure of protostars with the equation of state comprising both phases
and find maximum masses below 1.6 solar masses. Metastable heavy hybrid
protostars are not found.
