We present results of calculations which incorporate the effect of massive Dirac neutrinos in numerical models for the cooling of the neutron star associated with SN1987A. In the Weinberg-Salam standard model, minimally extended to include Dirac neutrino masses, the production of sterile (positive helicity) neutrinos via neutral-current neutrino-nucleon scattering proceeds at a rate that significantly affects the energetics of cooling. We determine the expected number of events, total energy in neutrinos and the burst duration for both Kamiokande II and Irvine-Michigan-Brookhaven detectors. Due to an increase in the cooling rate caused by sterile neutrinos, we find that for mν= mν2+mν2≥14 keV, the expected neutrino burst is shortened t o a duration that is inconsistent with the observations reported by both detectors. The calculations incorporate the feedback effects of the cooling due to sterile neutrinos in a self-consistent manner and the mass limit obtained is found to be largely insensitive to the equation of state used. © 1990.