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In this work we present a newly constructed equation of state (EoS), applicable to stellar core collapse and neutron star mergers including the entire baryon octet. Our EoS is compatible with the main constraints from nuclear physics and, in particular, with a maximum mass for cold β-equilibrated neutron stars of 2M⊙ in agreement with recent observations. As an application of our new EoS, we compute numerical stationary models for rapidly (rigidly) rotating hot neutron stars. We consider maximum masses of hot stars, such as protoneutron stars or hypermassive neutron stars in the postmerger phase of binary neutron star coalescence. The universality of I-Q relations at nonzero temperature for fast rotating models, comparing a purely nuclear EoS with its counterparts containing Λ hyperons or the entire baryon octet, respectively, is discussed, too. We find that the I-Q universality is broken in our models when thermal effects become important, independent on the presence of entropy gradients. Thus, the use of I-Q relations for the analysis of protoneutron stars or merger remnant data, including gravitational wave signals from the last stages of binary neutron star mergers, should be regarded with care. [ABSTRACT FROM AUTHOR]