It is argued that the most plausible source of power for the geodynamo is gravitational energy released by the growth of the solid inner core, and the essential features of this mechanism are outlined. The thermal regimes of the outer core which are possible if the dynamo is gravitationally powered are studied, and a number of interesting possibilities are found. First, if the liquidus gradient TL' is less than the conduction gradient TC', a slurry must occur in the fluid at the bottom of the outer core. Second, it is shown that compositionally driven convection can occur even if the actual temperature gradient T' is less than the adiabat TA'. This allows the possibility that heat may be transferred radially inward by the motions. Hence there is no direct relation between the rate that heat is conducted outward in the core and the rate of heat transfer to the mantle. Third, it is found that Higgins and Kennedy's hyppothesis does not preclude convective overturning driven by compositional buoyancy provided the thermal conductivity of the outer core is sufficiently large. Fourth, a slurry in the bulk of the outer core is stabilizing and incompatible with a convectively driven dynamo of any kind. It is argued that the gravitationally powered dynamo is possible only if the composition of the core is more metallic than the eutectic. The thermal evolution of the earth is considered, and it is found that if TA'C', the heat transfer problems for th core and mantle decouple with conditions in the core leading to a prescribed temperature at the base of the mantle and the mantle then prescribing the heat flux which must emanate from the core. It is shown that if T'=TL', a large flux of heat may flow from the core with virtually no change in temperature.