Recent radar observations from the European Space Agency's Mars Express spacecraft have been interpreted as evidence for melting beneath the ice at the south pole of Mars. We model the temperatures in the subsurface to determine the necessary conditions to achieve liquid water at the base of the ice cap. Salts lower the melting point of ice, with calcium‐perchlorate generating the lowest temperatures at which melting can be achieved. However, even if there are local concentrations of large amounts of these salts at the base of the south polar ice, typical Martian conditions are too cold to melt the ice. We find that a local heat source within the crust is needed to increase the temperatures, and a magma chamber within 10 km of the ice could provide such a heat source. This result suggests that if the liquid water interpretation of the observations is correct, magmatism on Mars may have been active extremely recently.