The general statement that hypothetical strange quark matter stars cool more rapidly than neutron stars is investigated in greater detail. It is found that the direct Urca process can be forbidden not only in neutron stars, but also in strange-matter stars. In this case, strange-matter stars cool slowly and their surface temperatures are more or less indistinguishable from those of slowly cooling neutron stars. We investigate the case of enhanced cooling again. We find that strange-matter stars cool significantly more rapidly than neutron stars within the first ～30 yr after birth. This result may become particularly interesting if continued observation of SN 1987A reveals the temperature of the pulsar that may reside at its center.
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