Are strange stars distinguishable from neutron stars by their cooling behaviour?

The general statement that strange 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. If so, strange stars would be slowly cooling and their surface temperatures would be more or less indistinguishable from those of slowly cooling neutron stars. The case of enhanced cooling is reinvestigated as well. It is found 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 centre.