  As neutron stars spin-down and contract, the deconfinement phase transition
can continue to occur, resulting in energy release(so-called deconfinement
heating) in case of the first-order phase transition. The thermal evolution of
neutron stars is investigated to combine phase transition and the related
energy release self-consistently. We find that the appearance of deconfinement
heating during spin-down result in not only the cooling delay but also the
increase of surface temperature of stars. For stars characterized by
intermediate and weak magnetic field strength, a period of increasing surface
temperature could exist. Especially, a sharp jump in surface temperature can be
produced as soon as quark matter appears in the core of stars with a weak
magnetic field. We think that this may serve as evidence for the existence of
deconfinement quark matter. The results show that deconfinement heating
facilitates the emergence of such characteristic signature during the thermal
evolution process of neutron stars.
