The effect of elevated temperature on the structural stability of Mo/Si, Mo2C/Si and Mo/Mo2C/Si/Mo2C (dMo2C equals 0.6 nm) multilayers was investigated. The multilayers deposited by dc magnetron sputtering are annealed at temperatures ranging from 200 degree(s)C to 700 degree(s)C. The multilayer mirrors were designed for normal incidence reflectivity at about 13 nm wavelength. X-ray scattering, transmission electron microscopy and atomic force microscopy were used for characterization of the multilayer structures. The results are correlated to the measured normal incidence reflectivity using synchrotron radiation. We achieved maximal normal incidence reflectivities of 61.8% at 13.0 nm wavelength for Mo2C/Si and 59.9% at 13.3 nm for Mo/Si multilayers having Mo2C diffusion barriers. While the reflectivity of Mo/Si multilayers decreased considerably after annealing above 300 degree(s)C the Mo2C/Si multilayers showed a superior thermal stability up to 600 degree(s)C.