  We apply the recently developed Log N - Log S test of compact star cooling
theories for the first time to hybrid stars with a color superconducting quark
matter core. While there is not yet a microscopically founded superconducting
quark matter phase which would fulfill constraints from cooling phenomenology,
we explore the hypothetical 2SC+X phase and show that the magnitude and
density-dependence of the X-gap can be chosen to satisfy a set of tests:
temperature - age (T - t), the brightness constraint, Log N - Log S, and the
mass spectrum constraint. The latter test appears as a new conjecture from the
present investigation.
