Due to their unique set of multimessenger signals, neutron star mergers have emerged as a novel environment for studies of new physics beyond the Standard Model (SM). As a case study, we consider the simplest extension of the SM scalar sector involving a light CP-even scalar singlet S mixing with the SM Higgs boson. These S particles can be produced abundantly in neutron star mergers via the nucleon bremsstrahlung process. We show that the S particles may either be trapped in or stream freely out of the merger remnant, depending on the S mass, its mixing with the SM Higgs boson, and the temperature and baryon density in the merger. In the free-streaming region, the scalar S will provide an extra channel to cool down the merger remnant, with cooling timescales as small as O(ms). On the other hand, in the trapped region, the Bose gas of S particles could contribute a larger thermal conductivity than the trapped neutrinos in some parts of the parameter space, thus leading to faster thermal equilibration than expected. Therefore, future observations of the early postmerger phase of a neutron star merger could effectively probe a unique range of the S parameter space, largely complementary to the existing and future laboratory and supernova limits. In view of these results, we hope the merger simulation community will be motivated to implement the effects of light CP-even scalars into their simulations in both the free-streaming and trapped regimes.