1] The presence of the global magnetic field of Mercury has implications for the interior structure of the planet and its thermal evolution. We use a thermal evolution model to explore the conditions under which excess entropy is available to drive a convective dynamo. The current state of the core is strongly affected by its sulfur concentration and the viscosity of the overlying mantle. A present-day dynamo is difficult to achieve. The minimum rate of entropy production required to drive a dynamo is attained in only the most optimistic models, and requires present-day mantle convection. An additional entropy source such as the addition of a radiogenic heat source in the core increases the probability of a present-day dynamo. Given the uncertainty, more specific characterization of the planet's interior and magnetic field is required to alleviate ambiguities in the original Mariner 10 observations.