ABSTRACT Measuring the time evolution of the effective surface temperature of neutron stars can provide invaluable information on the properties of their dense cores. Here, we report on a new Chandra observation of the transient neutron star low-mass X-ray binary HETE J1900.1–2455, which was obtained ≈2.5 yr after the end of its ≈10-yr long accretion outburst. The source is barely detected during the observation, collecting only six net photons, all below 2 keV. Assuming that the spectrum is shaped as a neutron star atmosphere model, we perform a statistical analysis to determine a 1σ confidence upper range for the neutron star temperature of ≈30–39 eV (for an observer at infinity), depending on its mass, radius, and distance. Given the heat injected into the neutron star during the accretion outburst, estimated from data provided by all-sky monitors, the inferred very low temperature suggests that the core either has a very high heat capacity or undergoes very rapid neutrino cooling. While the present data do not allow us to disentangle these two possibilities, both suggest that a significant fraction of the dense core is not superfluid/superconductor. Our modelling of the thermal evolution of the neutron star predicts that it may still cool further, down to a temperature of ≃15 eV. Measuring such a low temperature with a future observation may provide constraints on the fraction of baryons that is paired in the stellar core.