Primary magmas form by partial melting in the mantle of a terrestrial planet and represent the starting material for building its crust. The compositions of primary magmas are critical for understanding the thermal history of planetary interiors, as they can be used to estimate mantle potential temperatures (TP) and track changes in the conditions of mantle partial melting over time. Here, we introduce PRIMARSMELT, a new member of the PRIMELT software family, calibrated to estimate the composition of Martian primary magmas and their formation conditions. We applied PRIMARSMELT to a comprehensive database of basaltic compositions from Mars. Our results are consistent with their petrology, requiring olivine addition to restore fractionated compositions to their primary parents and olivine subtraction from cumulate rocks. Individual primary magma solutions provide insights into the petrogenesis of specific Martian meteorites, with implications for the near‐primary nature of some primitive meteorites and the relationship between lithologies A and B in meteorite EETA 79001. Taken together, our results suggest nearly constant or potentially increasing mantle potential temperatures throughout the geological history of Mars. The average TP for young shergottite meteorites is ∼1,442 ± 40°C, similar to ambient mantle temperatures inferred from geophysical models. In contrast, older basaltic rocks record potential temperatures as low as ∼1,320 ± 48°C for igneous clasts in meteorites NWA 7034/7533. We suggest that, rather than plume‐related magmatism, shergottite meteorites record ambient mantle temperatures, with the thermal evolution trend possibly resulting from inefficient heat loss, as expected for a planet in stagnant‐lid mode.