We investigate the properties of the color-flavor-locked (CFL) quark matter and quark stars (QSs) at finite temperature and under strong magnetic fields within the MIT bag model. We find that the free energy per baryon, energy density, and pressure depend strongly on temperature, thereby affecting the properties of CFL quark stars at finite temperature. The equation of CFL quark matter is stiffen by the increasing temperature, and the pressure becomes anisotropic under strong magnetic fields. For the isentropic stages, the maximum star mass at finite temperature increases with the value of the entropy per baryon. Furthermore, the polytropic index of CFL quark star matter decreases with the increment of the star mass, while the temperature of the star matter increases with the entropy per baryon. Our results also indicate that the thermodynamic quantities of the CFL quark matter may exhibit distinct dependencies on temperature and magnetic fields.