  We construct a new isentropic equation of state (EOS) at finite temperature
"CRover" on the basis of the hadron-quark crossover at high density. By using
the new EOS, we study the structure of hot neutron stars at birth with the
typical lepton fraction ($Y_l=0.3-0.4$) and the typical entropy per baryon
($S=1-2$). Due to the gradual appearance of quark degrees of freedom at high
density, the temperature T and the baryon density at the center of the hot
neutron stars with the hadron-quark crossover are found to be smaller than
those without the crossover by a factor of 2 or more. Typical energy release
due to the contraction of a hot neutron star to a cold neutron star with 1.4
solarmass is shown to be about 0.04 solarmass with the spin-up rate about 14%.
