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Terrestrial planets cool over geological time through conduction and convection, with cooling rates inversely proportional to planetary radius. Radiogenic heating from long-lived isotopes (U, Th, K-40) sustains mantle convection and surface volcanism for billions of years.
Use thermal history models for Earth, Moon, Mars, and Mercury to show why planet size determines thermal longevity. Compare expected core cooling timescales with observed magnetic field durations.
From your study of planetary interiors, you know that terrestrial planets formed hot — heated by accretional impacts, gravitational compression, and the decay of short-lived radioactive isotopes. From thermal conductivity, you know that heat moves through rock slowly by conduction and much more efficiently by convection when temperature gradients are steep enough. The thermal evolution of a planet is the story of how it loses this primordial heat over billions of years, and the critical insight is that planet size controls the pace.
The reason is geometry. A planet's heat content scales with its volume (proportional to radius cubed), but heat escapes through its surface (proportional to radius squared). The ratio of volume to surface area grows linearly with radius, so larger planets retain heat far longer than smaller ones. This is why Earth, at roughly 12,700 km in diameter, still has a vigorously convecting mantle and an active magnetic field after 4.5 billion years, while the Moon (3,474 km) and Mercury (4,880 km) cooled through their interiors relatively quickly and are now largely geologically dead. Mars (6,779 km) sits in between — it lost its global magnetic field billions of years ago as its core cooled below the threshold for dynamo action, but residual heat still drives occasional volcanism.
Radiogenic heating from long-lived isotopes — uranium-238, thorium-232, and potassium-40 — is the second major factor. These isotopes have half-lives of billions of years, so they continue producing heat long after the planet's primordial heat would otherwise have dissipated. In Earth, radiogenic heating contributes roughly half of the total internal heat flux today, sustaining mantle convection and plate tectonics. Without it, Earth's interior would have cooled much further by now. The concentration of these isotopes depends on a planet's bulk composition, which in turn depends on the materials available during formation — another link back to protoplanetary disk chemistry.
Cooling does not proceed at a constant rate. Early in a planet's history, when the interior is hottest and temperature gradients are steepest, convection is vigorous and heat loss is rapid. As the interior cools, convection slows, the mantle stiffens, and heat loss transitions increasingly toward conduction through a thickening lithosphere. This creates a feedback: slower cooling means the remaining heat is retained even longer. Some planets may develop a stagnant lid regime where the entire surface is a single rigid plate (like Mars and Venus today), dramatically reducing heat loss compared to Earth's plate tectonics, which efficiently recycles cool surface material back into the hot interior. The thermal state of a planet at any given time determines whether it has volcanism, a magnetic field, plate tectonics, or an atmosphere replenished by outgassing — making thermal evolution one of the most consequential processes in planetary science.