2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110433We review the status of research on the cooling of compact stars, with emphasis on the influence of color superconducting quark matter phases. Although a consistent microscopic approach is not yet available, severe constraints on the phase structure of matter at high densities come from recent mass and cooling observations of compact stars.11 pages, 9 figures, to be published in the Proceedings of the Johns Hopkins Workshop on 'Strong Matter in the Heaven', Budapest, August 1-3, 2005Nuclear Theorytext