We study the effect of dark matter heating on the temperature of typical strange star(SS hereafter)(M=1.4 M⊙,R=10 km)in normal phase(NSS hereafter)and in a possible existing colour-flavour locked(CFL)phase(CSS hereafter).For NSS,the influence of dark matter heating is ignored until roughly 107yr.After 107yr,the dark matter heating is dominant that significantly delays the star cooling,which maintains a temperature much higher than that predicted by standard cooling model for old stars.Especially for CSS,the emissivity of dark matter will play a leading role after roughly 104yr,which causes the temperature to rise.This leads to the plateau of surface temperature appearing in～106.5yr which is earlier than that of NSS(～107yr).
