Abstract: The paper defines the characteristics of two proto-quark stars (M_b=1.22M_? and M_b=1.62M_(?"\ " )) that were formed after the explosion of the supernova. It is assumed that the changes in the energy and lepton charge of the central regions of the pre-supernova star can be neglected during the implosion. The equation of state for hot quark matter is determined based on the MIT bag theory taking into account the presence of neutrinos. The possible maximum values of the central temperatures of these stars are determined. The energy of neutrinos in the studied proto-quark stars is of the order of 250-300 MeV. The decrease in the mass of these stars during cooling is about 0.16 for M_b=1.22M_? and 0.25 for M_b=1.62M_(?"\ " ).