Reconstruction of the geological history of Mars has been the focus of considerable attention over the past four decades, with important discoveries being made about variations in surface conditions(1). However, despite a significant increase in the amount of data related to the morphology, mineralogy and chemistry of the martian surface, there is no clear global picture of how magmatism has evolved over time and how these changes relate to the internal workings and thermal evolution of the planet. Here we present geochemical data derived from the Gamma Ray Spectrometer on board NASA's Mars Odyssey spacecraft(2), focusing on twelve major volcanic provinces of variable age. Our analysis reveals clear trends in composition that are found to be consistent with varying degrees of melting of the martian mantle. There is evidence for thickening of the lithosphere (17-25 km Gyr(-1)) associated with a decrease in mantle potential temperature over time (30-40 K Gyr(-1)). Our inferred thermal history of Mars, unlike that of the Earth, is consistent with simple models of mantle convection(3-6).