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We present the novel finite-temperature FSU2H* equation-of-state model that covers a wide range of temperatures and lepton fractions for the conditions in proto-neutron stars, neutron star mergers and supernovae. The temperature effects on the thermodynamical observables and the composition of the neutron star core are stronger when the hyperonic degrees of freedom are considered. We pay a special attention to the temperature and density dependence of the thermal index in the presence of hyperons and conclude that the true thermal effects cannot be reproduced with the use of a constant Г law

We review the composition and the equation of state of the hyperonic core of neutron stars at finite temperature within a relativistic mean-field approach. We make use of the new FSU2H∗ model, which is built upon the FSU2H scheme by improving on the Ξ potential according to the recent analysis on the Ξ atoms, and we extend it to include finite temperature corrections. The calculations are done for a wide range of densities, temperatures and charge fractions, thus exploring the different conditions that can be found in protoneutron stars, binary mergers remnants and supernovae explosions. The inclusion of hyperons has a strong effect on the composition and the equation of state at finite temperature, which consequently would lead to significant changes in the properties and evolution of hot neutron stars.