  The presence of the color-flavor locked (CFL) phase strongly suppresses the
neutrino emission processes and the quark specific heat. As a result the
cooling of the strange stars in the CFL phase is dominated by deconfinement
heating and surface emission. The temperature of these stars with strong
magnetic field ($B{\geq}10^{10}G$) rise significantly during the first several
ten or hundred years, which may be an effective signature of strange stars as
implicated by pulsar 0540-69. Furthermore a limit line is predicted, which
means compact stars have an upper limit temperature at any moment. We still may
search for the candidates for strange stars in the CFL phase along the limit
line.
  The presence of the color-flavor locked (CFL) phase strongly suppresses the
neutrino emission processes and the quark specific heat. As a result the
cooling of the strange stars in the CFL phase is dominated by deconfinement
heating and surface emission. The temperature of these stars with strong
magnetic field ($B{\geq}10^{10}G$) rise significantly during the first several
ten or hundred years, which may be an effective signature of strange stars as
implicated by pulsar 0540-69. Furthermore a limit line is predicted, which
means compact stars have an upper limit temperature at any moment. We still may
search for the candidates for strange stars in the CFL phase along the limit
line.
