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ABSTRACT The thermal evolution of hypernuclear compact stars is studied for stellar models constructed on the basis of covariant density functional theory in Hartree and Hartree–Fock approximation. Parametrizations of both types are consistent with the astrophysical mass constraints on compact stars and available hypernuclear data. We discuss the differences of these density functionals and highlight the effects they have on the composition and on the cooling of hypernuclear stars. It is shown that hypernuclear stars computed with density functional models that have a low symmetry energy slope, L, are fairly consistent with the cooling data of observed compact stars. The class of stellar models based on larger L values gives rise to the direct Urca process at low densities, which leads to significantly faster cooling. We conjecture high-density pairing for protons and Λ’s in the P-wave channel and provide simple scaling arguments to obtain these gaps. As a consequence the most massive stellar models with masses 1.8 ≤ M/M⊙ ≤ 2 experience slower cooling by hyperonic dUrca processes which involve Λ’s and protons.