Molybdenum-Carbon multilayer structures are investigated for their thermal stability as these are of interest in the energy range of 3-18 keV, a spectrum available from most of the wigglers/undulators of synchrotron radiation sources at a relatively higher power. Mo/C multilayer structures with a period of 50 Angstrom are prepared by electron beam evaporation in ultra high vacuum environment. X-ray reflectivity and X-ray diffraction studies at a wavelength of 1.542 Angstrom are used for investigation. The multilayer structure is stable up to 750 degrees C and the expansion in period is similar to 2.3%. The multilayer structure is destroyed at 850 degrees C due to the crystallization of molybdenum carbides. Possible reasons for the high thermal stability and low period expansion compared to other metal/C multilayer structures are discussed.