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We assess the impact of accurate, self-consistent modelling of thermaleffects in neutron-star merger remnants in the context of third-generationgravitational-wave detectors. This is done through the usage, in Bayesian modelselection experiments, of numerical-relativity simulations of binary neutronstar (BNS) mergers modelled through: a) nuclear, finite-temperature (or``tabulated'') equations of state (EoSs), and b) their simplifed piecewise (or``hybrid'') representation. These cover four different EoSs, namely SLy4, DD2,HShen and LS220. Our analyses make direct use of the Newman-Penrose scalar$\psi_4$ outputted by numerical simulations. Considering a detector networkformed by three Cosmic Explorers, we show that differences in thegravitational-wave emission predicted by the two models are detectable with anatural logarithmic Bayes Factor $\log{\cal{B}}\geq 5$ at average distances of$d_L \simeq 50$Mpc, reaching $d_L \simeq 100$Mpc for source inclinations $\iota\leq 0.8$, regardless of the EoS. This impact is most pronounced for the HShenEoS. For low inclinations, only the DD2 EoS prevents the detectability of suchmodelling differences at $d_L \simeq 150$Mpc. Our results suggest that theusage a self-consistent treatment of thermal effects is crucial forthird-generation gravitational wave detectors.

Self-consistent treatment of thermal effects in neutron-star  post-mergers: observational implications for third-generation  gravitational-wave detectors