Which geophysical process, driven by Earth's internal heat, regulates carbon dioxide levels over geological timescales?

Plate tectonics and volcanism.

The long-term stability of Earth's climate, particularly regarding surface temperature regulation, is maintained by the carbon-silicate cycle, a process heavily reliant on plate tectonics and associated volcanism. Volcanic activity releases carbon dioxide, a critical greenhouse gas, back into the atmosphere from the planet's interior. Concurrently, weathering processes draw CO2 out of the atmosphere and sequester it into carbonate rocks which are then subducted via plate movement. This recycling mechanism acts as a planetary thermostat, preventing the atmosphere from either freezing over or overheating due to accumulating CO2, a process that may cease on smaller, cooler rocky worlds as their internal heat dissipates.