The subsolidus convective cooling histories of terrestrial planets evolving from hot initial states are investigated with a simple analytic model which simulates the average heat transport in a vigorously convecting mantle devoid of internal heat sources. The temperature dependence of the effective viscosity of mantle rocks is the single most important factor controlling thermal history. It is responsible for the growth of the rigid lithosphere, a rheological and thermal boundary layer, and serves the function of a thermostat, regulating the rate of cooling by the negative feedback between viscosity and temperature. Except for a relatively short period of time when mantle temperature decreases rapidly during the early stages of cooling, a planet cools mainly by thickening its lithosphere; the underlying mantle temperature decreases relatively slowly. On one-plate planets, the growth of a rigid lithosphere involves an imbalance between the surface heat flux and the heat flow from the mantle; the former is always larger than the latter. Primordial heat can contribute substantially, e.g., as much as about a fourth or a third, to the present surface heat flux of a planet. For both these reasons, the radiogenic heat source content of a planet is likely to be overestimated by inferences from surface heat flow observations.

Although vigorous mantle convection early in the thermal history of the Earth is shown to be capable of removing several times the latent heat content of the core, we are able to construct a thermal evolution model of the Earth in which the core does not solidify. The large amount of energy removed from the model Earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the Earth, and the cores of these planets may not possess enough internal energy to prevent core solidification by mantle convection. Our models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The Earth models are constrained by the present surface heat flux and mantle viscosity. Internal heat sources produce only about 55% of the Earth model's present surface heat flow.

Numerical calculations of the dynamical ellipticity of the moon due to finite amplitude solid state convection indicate that convection could be the cause of the non‐hydrostatic gravitational figure, but only if the lunar lithosphere is capable of resisting global scale deformation. Thus lithospheric inhomogeneities and surface loads could also contribute substantially to the disequilibrium of the gravity figure. The calculations also show that it is unlikely that the geometrical distortion is due to convection.

Thermal models of the Moon, which include cooling by subsolidus creep and consideration of the creep behaviour of geologic material, provide estimates of 1500- 1600 K for the temperature, and 10 21-1022 cm2/s for the viscosity of the deep lunar interior.