Oxygen-free high-conductivity copper (OFHC), chromium-zirconium copper (CuCrZr), and Glidcop®AL-15 are widely used in the high heat load absorber elements at the front end of synchrotron radiation facilities. It is necessary to choose the most suitable material according to the actual engineering conditions (such as the specific heat load, material performance, and costs). In the long-term service period, the absorber elements have to bear hundreds or kilowatts of high heat load and its “load-unload” cyclic loading mode. Therefore, the thermal fatigue and thermal creep properties of the materials are critical and have been extensively studied. In this paper, based on the published pieces of the literature, the thermal fatigue theory, experimental principles, methods, test standards, test types of equipment, and key indicators of the thermal fatigue performance of typical copper metal materials used in the front end of synchrotrons radiation Facilities are reviewed, as well as the relevant studies carried out by the well-known synchrotron radiation institutions. In particular, the fatigue failure criteria for these materials and some effective methods for improving the thermal fatigue resistance performance of the high-heat load components are also presented.