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Rotochemical heating originates in a departure from beta equilibrium due tospin-down compression in a rotating neutron star. The main consequence is thatthe star eventually arrives at a quasi-equilibrium state, in which the thermalphoton luminosity depends only on the current value of the spin-down power,which is directly measurable. Only in millisecond pulsars the spin-down powerremains high long enough for this state to be reached with a substantialluminosity. We report an extensive study of the effect of this heatingmechanism on the thermal evolution of millisecond pulsars, developing a generalformalism in the slow-rotation approximation of general relativity that takesthe spatial structure of the star fully into account, and using a sample ofrealistic equations of state to solve the non-superfluid case numerically. Weshow that nearly all observed millisecond pulsars are very likely to be in thequasi-equilibrium state. Our predicted quasi-equilibrium temperatures for PSRJ0437-4715 are only 20% lower than inferred from observations. Accounting forsuperfluidity should increase the predicted value.Comment: 34 pages, 8 figures, AASTeX. Accepted for publication in Ap

Rotochemical Heating in Millisecond Pulsars: Formalism and Nonsuperfluid Case