If an axion of mass between about 10(exp -3) eV and 1 eV exists, axion emission would have significantly affected the cooling of the nascent neutron star associated with SN 1987A. For an axion of mass less than about 10(exp -2) eV, axions produced deep inside the neutron star simply stream out; in a previous paper this case has been addressed. Remarkably, for an axion of mass greater than about 10(exp -2) eV axions would, like neutrinos, have a mean-free path that is smaller than the size of a neutron star, and thus would become 'trapped' and radiated from an axion sphere. In this paper the trapping regime is treated by using numerical models of the initial cooling of a hot neutron star that incorporate a leakage approximation scheme for axion-energy transport. The axion opacity is computed due to inverse nucleon-nucleon, axion bremsstrahlung, and numerical models are used to calculate the integrated axion luminosity, the temperature of the axion sphere, and the effect of axion emission on the neutrino bursts detected by the Kamiokande 2 (K2) and Irvine-Michigan-Brookhaven (IMB) water-Cherenkov detectors. The larger the axion mass, the stronger the trapping and the smaller the axion luminosity. The earlier estimate is confirmed and refined of the axion mass above which trapping is so strong that axion emission does not significantly affect the neutrino burst. Based upon the neutrino-burst duration--the most sensitive barometer of axion cooling--it is concluded that for an axion mass of greater than about 0.3 eV, axion emission would not have had a significant effect on the neutrino bursts detected by K2 and IMB. The present work, together with the previous work, strongly suggests that an axion with mass in the interval 10(exp -3) eV to 0.3 eV is excluded by SN 1987A.