Helium white dwarf in PSR J0751+1807; too cool, in PSR J1012+5307; too   hot?
  We discuss the cooling history of the low-mass, helium core white dwarfs in short orbital period millisecond pulsars PSR J0751+1807 and PSR J1012+5307. The revised cooling age estimated by Alberts et al. agrees with the age estimation for PSR J1012+5307, removing the discrepancy between the spin-down age and the cooling age. However, if we accept this model then the helium white dwarf in the binary pulsar system PSR J0751+1807 must be much hotter than is observed. We propose that this discrepancy may be resolved if, after detachment of the secondary star from its Roche lobe in PSR J0751+1807, the star loses its hydrogen envelope due to pulsar irradiation. When hydrogen burning stops, the white dwarf will cool down much more quickly than in the case of a thick hydrogen envelope with a hydrogen burning shell. We discuss several possibilities to explain different cooling histories of white dwarfs in both systems. 
Ene Ergma (Physics Department, Tartu University), Marek J. Sarna (N.   Copernicus Astronomical Center) and Jelena Gerskevits...