We present two recent parametrizations of the equation of state (FSU2R and FSU2H models) that reproduce the properties of nuclear matter and finite nuclei, fulfill constraints on high-density matter stemming from heavy-ion collisions, produce 2M⊙ neutron stars, and generate neutron star radii below 13 km. Making use of these equations of state, cooling simulations for isolated neutron stars are performed. We find that two of the models studied, FSU2R (with nucleons) and, in particular, FSU2H (with nucleons and hyperons), show very good agreement with cooling observations, even without including nucleon pairing. This indicates that cooling observations are compatible with an equation of state that produces a soft nuclear symmetry energy and, thus, generates small neutron star radii. Nevertheless, both schemes produce cold isolated neutron stars with masses above 1.8M⊙.
