Solar Wind (SW) electron precipitation is able to deposit a substantial amount of energy in the nightside Martian upper atmosphere, potentially exerting an influence on its thermal structure. This study serves as the first investigation of such an issue, with the aid of the simultaneous measurements of both neutral density and energetic electron intensity made on board the recent Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft. We report that, from a statistical point of view, the existing measurements do not support a scenario of noticeable neutral heating via SW electron precipitation. However, during 3%−4% of the MAVEN orbits for which data are available, strong correlation between nightside temperature and electron intensity is observed, manifested as collocated enhancements in both parameters, as compared to the surrounding regions. In addition, our analysis also indicates that neutral heating via SW electron precipitation tends to be more effective at altitudes below 160 km for integrated electron intensities above 0.01 ergs·cm−2·s−1 over the energy range of 3−450 eV. The results reported here highlight the necessity of incorporating SW electron precipitation as a heat source in the nightside Martian upper atmosphere under extreme circumstances such as during interplanetary coronal mass ejections.