  We have considered a hot neutron star with a quark core, a mixed phase of
quark-hadron matter, and a hadronic matter crust and have determined the
equation of state of the hadronic phase and the quark phase, we have then found
the equation of state of the mixed phase under the Gibbs conditions. Finally,
we have computed the structure of hot neutron star with the quark core and
compared our results with those of the neutron star without the quark core. For
the quark matter calculations, we have used the MIT bag model in which the
total energy of the system is considered as the kinetic energy of the particles
plus a bag constant. For the hadronic matter calculations, we have used the
lowest order constrained variational (LOCV) formalism. Our calculations show
that the results for the maximum gravitational mass of the hot neutron star
with the quark core are substantially different from those of without the quark
core.
