As a strange star spins down, its core density increases, changing the
chemical equilibrium state of strange matter. The relaxation toward t
he new equilibrium state takes a finite time, so the matter is not qui
te in chemical equilibrium, and energy is released by reactions at the
expense of the stored chemical energy. We study such a chemical heati
ng process for a spin-down strange star and find that this effect is s
ignificant at later times for weak magnetic fields. We compare the coo
ling of a strange star with that of an ordinary neutron star and find
that the surface temperature of the strange star is much lower than th
at of the neutron star at the age up to 10(8) yr. This favorable to an
observational signature for strange stars.