The Mars thermosphere holds clues to the evolution of the Martian climate and has practical implications for spacecraft visiting Mars, which often use it for aerobraking upon arrival, or for landers, which must pass through it. Nevertheless, it has been sparsely characterized, even when past accelerometer measurements and remote observations are taken into account. The Mars Atmosphere and Volatile EvolutioN (MAVEN) orbiter, which includes a number of instruments designed to characterize the thermosphere, has greatly expanded the available thermospheric observations. This paper presents new and unanticipated measurements of density and temperature profiles (120–200 km) derived from solar occultations using the MAVEN Extreme Ultraviolet (EUV) Monitor (EUVM). These new measurements complement and expand MAVEN's intended thermospheric measurement capacity. In particular, because the local time is inherently fixed to the terminator, solar occultations are ideally suited for characterizing long‐term and latitudinal variability. Occultation measurements are made during approximately half of all orbits, resulting in thousands of new thermospheric profiles. The density retrieval method is presented in detail, including an uncertainty analysis. Altitude‐latitude maps of thermospheric density and temperature at perihelion and aphelion are presented, revealing structures that have not been previously observed. Tracers of atmospheric dynamics are also observed, including (1) a high altitude polar warming feature at intermediate latitudes, (2) cooler temperatures coinciding with increased gravity wave activity, and (3) an apparent thermostatic response to solar EUV heating during a solar rotation, which shows heating at high altitudes that is accompanied by cooling at lower altitudes.