The presence of superfluidity in neutron star interiors can affect the cooling of neutron stars in intricate ways, enhancing certain mechanisms and suppressing others. Model calculations employing realistic nuclear potentials in Bardeen–Cooper–Schrieffer theory generally suggest the development of a 3P2–3F2 pairing gap, and therefore the presence of superfluidity in dense neutron star matter. Improved models that go beyond conventional mean-field calculations by including polarization effects suggest a suppression of the triplet gap. We have evaluated the pairing interaction by summing the “parquet” Feynman diagrams, which include both ladder and ring diagrams systematically, plus a set of important nonparquet diagrams, making this the most comprehensive diagram-based approach presently available. Our results suggest a radical suppression of the 3P2–3F2 triplet pairing gap and an enhancement of 3P0 pairing.