  The study of thermal emission from isolated, cooling neutron stars plays a
key role in probing the physical conditions of both the star crust and the
core. The comparison of theoretical models for the star thermal evolution with
the surface temperature derived from X-ray observations of sources of different
age is one of the main tools to investigate the properties of the interior and
constrain the equation of state. Here we propose to use population synthesis
studies as an independent approach to test the physics governing the star
cooling. Theoretical Log N - Log S distributions depend on the assumed neutron
star thermal evolution. We have computed distributions for several different
cooling scenarios and found that comparison with the observed Log N - Log S of
isolated neutron stars is effective in discriminating among cooling models.
Among the eleven cooling models considered in this paper, all of which may
reproduce the observed temperature vs. age diagram, only at most three can
explain the Log N - Log S distribution of close-by cooling neutron stars. The
Log N - Log S test, being a ``global'' one and despite some limitations,
appears capable of complementing the standard temperature vs. age test used up
to now.
