The forthcoming lunar exploration of Chang’e-5 (CE-5) mission will be the first sampling return project of China. The actual drilling needs the information about real-time illumination and corresponding temperature. To give a support for the project, in this paper the SPICE software system is first used to calculate the real-time illumination at the CE-5 candidate landing site Mons Rümker. It is found that our synthetic map of illumination is consistent with the morning map of illumination provided by the Japan’s SELENE satellite. This result verifies the rationality of our algorithm and the corresponding code. According to the calculated illumination and considering a one-dimensional heat conduction model, we study the temperature distribution over Mons Rümker. It is found that the regolith temperature near the surface is greatly related to the illumination, but varies a little with the depth increasing. It is also discovered that the regolith temperature beneath a depth of 0.57 m will not change any more. To give a support for the actual drilling program, it is recommended to consider the temperature difference between the outside and inside of the regolith, especially their stresses caused by such a temperature difference. Moreover, considering the drilling depth of CE-5 larger than 0.57 m, it is likely to measure the heat flow for the constant-temperature layer. We propose that for the next lunar exploration following CE-5 the measurement of heat flow is considered. This will promote the research of lunar science.