  A collection of modern, field-theoretical equations of state is applied to
the investigation of cooling properties of compact stars. These comprise
neutron stars as well as hypothetical strange matter stars, made up of
absolutely stable 3-flavor strange quark matter. Various uncertainties in the
behavior of matter at supernuclear densities, e.g., hyperonic degrees of
freedom, behavior of coupling strengths in matter, pion and meson condensation,
superfluidity, transition to quark matter, absolute stability of strange quark
matter, and last but not least the many-body technique itself are tested
against the body of observed cooling data.
