  As a neutron star spins down, the nuclear matter continuously is converted
into quark matter due to the core density increase and then latent heat is
released. We have investigated the thermal evolution of neutron stars
undergoing such deconfinement phase transition. We have taken into account the
conversion in the frame of the general theory of relativity. The released
energy has been estimated as a function of change rate of deconfinement baryon
number. Numerical solutions to cooling equation are obtained to be very
different from the without heating effect. The results show that neutron stars
may be heated to higher temperature which is well-matched with pulsar's data
despite onset of fast cooling in neutron stars with quark matter core. It is
also found that heating effect has magnetic field strength dependence. This
feature could be particularly interesting for high temperature of low-field
millisecond pulsar at late stage. The high temperature could fit the observed
temperature for PSR J0437-4715.
