Orbital observations of Mercury by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft provide new constraints on that planet's thermal and interior evolution. Specifically, MESSENGER observations have constrained the rate of radiogenic heat production via measurement of uranium, thorium, and potassium at the surface, and identified a range of surface compositions consistent with high-temperature, high-degree partial melts of the mantle. Additionally, MESSENGER data have placed new limits on the spatial and temporal variation in volcanic and tectonic activity and enabled determination that the planet's core is larger than previously estimated. Because Mercury's mantle layer is also thinner than previously thought, this result gives greater likelihood to the possibility that mantle convection is marginally supercritical or even that the mantle is not convecting. We simulate mantle convection and magma generation within Mercury's mantle under two-dimensional axisymmetry and a broad range of conditions to understand the implications of MESSENGER observations for the thermal evolution of the planet. These models demonstrate that mantle convection can persist in such a thin mantle for a substantial portion of Mercury's history, and often to the present, as long as the mantle is thicker than ~300 km. We also find that magma generation in Mercury's convecting mantle is capable of producing widespread magmas by large-degree partial melting, consistent with MESSENGER observations of the planet's surface chemistry and geology.