A collection of modem, held-theoretical equations of state is applied
to the investigation of cooling properties of compact stars. These com
prise neutron stars as well as hypothetical strange-matter stars, made
up of absolutely stable 3-flavor strange-quark matter. Various uncert
ainties in the behavior of matter at supernuclear densities, e.g., hyp
eronic degrees of freedom, behavior of coupling strengths in matter, p
ion and meson condensation, superfluidity, transition to quark matter,
absolute stability of strange-quark matter, and last but not least th
e many-body technique itself are tested against the body of observed c
ooling data.