  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 could be forbidden not only in neutron stars but
also in strange stars. In this case, strange stars are slowly cooling, and
their surface temperatures are more or less indistinguishable from those of
slowly cooling neutron stars. Furthermore the case of enhanced cooling is
reinvestigated. It shows that strange stars cool significantly more rapidly
than neutron stars within the first $\sim 30$ years after birth. This feature
could become particularly interesting if continued observation of SN 1987A
would reveal the temperature of the possibly existing pulsar at its center.
