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Published online by Cambridge University Press: 12 April 2016
It is accepted that formation of a binary millisecond (or recycled) pulsar with a low–mass companion may be explained as the end–point of close binary evolution in which an old pulsar is spun–up by accretion from the secondary (Alpar et al., 1982). After detachment from the Roche lobe, the pulsar spin period starts to change due to magneto–dipole radiation and the white dwarf begins to cool down. In this paper we shall discuss the cooling history of helium core low–mass white dwarfs in the short orbital period millisecond binary pulsars PSR J0751+1807 and PSR J1012+5307 (Ergma, Sarna, & Antipova 1999).