  We study the structure and evolution of neutron stars (NS) the interiors of
which are modeled using microscopic approaches and constrained by the condition
that the equation of state (EoS) of matter extrapolated to high densities
should not contradict known observational data from compact stars and
experimental data from heavy-ion collisions (HIC). We use modern cooling
simulations to extract distributions of NS masses required to reproduce those
of the yet sparse data in the Temperature-Age (TA) plane. By comparing the
results with a mass distribution for young, nearby NSs used in population
synthesis we can sharpen the NS cooling constraints.
