  We analyze the effect of magnetic field in superconducting neutron-star cores
on the chemical heating of millisecond pulsars (MSPs). We argue that the
magnetic field destroys proton superconductivity in some volume fraction of the
stellar core, thus allowing for unsuppressed non-equilibrium reactions of
particle mutual transformations there. The reactions transform the chemical
energy, accumulated by a neutron star core during the low-mass X-ray binary
stage, into heat. This heating may keep an NS warm at the MSP stage (with the
surface temperature $\sim 10^5\,\rm K$) for more than a billion of years after
ceasing of accretion, without appealing to the rotochemical heating mechanism.
