Heat transfer in the Earth's lithosphere
To geophysicists and tectonicists alike, the continental geotherm, i.e. the distribution of temperature with depth, is an important characteristics of the Earth's lithosphere because temperature impacts on all physical properties of rocks (e.g. density, viscosity, conductivity, elasticity, magnetism etc) and because temperature controls the rheology of rocks (i.e how they deform in response to applied deviatoric stresses) and therefore how the Earth's lithosphere reacts to tectonic forces.

The continental geotherm is a function of the i/ rate at which heat is produced or consumed within the lithosphere, ii/ the rate at which the lithosphere looses heat to the atmosphere/ocean system, and iii/ the rate at which the lithosphere gains heat from the convective mantle. When the heat lost by the lithosphere balances the heat gained by the lithosphere, an equilibrium is reached and the geotherm is said to be steady state (i.e. the temperature at any given depth does not change through time). In contrast, when the lithosphere has a net gain or a net loss of heat, the geotherm is said to be transient (i.e the temperature changes through time, until a new equilibrium is reached). On a billion year time scale, geotherms are always transient, however, at the scale of 100 myr, and in the absence of geological processes, geotherms can approach an equilibrium which express the balance between heat gained and heat lost by the lithosphere.

Here, we first review the processes involved in heat generation and heat transfer, and we derive from the rate of these processes a general equation which describes the change in temperature with depth and through time. From this general equation we derive a particular solution for the so called "steady state" continental geotherm (temperature changes with depth but not with time, i.e. zero net heat gain or loss). In a second part, we discuss how the steady state continental geotherm is affected by a number of geological processes including, lithospheric thinning and thickening, burial via sedimentary or volcanic processes, and basal heating via the spreading of mantle plumes at the base of the Earth's lithosphere.

Temperature and Heat
The temperature (degree of hotness or coldest) of a small volume of rock somewhere in the lithosphere varies if heat (a form of kinetic energy) is gained or lost. The relationship that gives the variation of temperature dT as a function of a variation of heat dE is: dT=dE/(Cp.m), with Cp the heat capacity, and m the mass. The main processes able to change the amount of heat contained in a small volume or rock in the lithosphere are:

• Heat conduction (transfer of kinetic energy between molecules or atoms)
• Heat advection (replacement of a volume at temperature T₁ with an equivalent volume at temperature T₂)
• Heat production (heat produced by radioactive isotopes, viscous heating, exothermic metamorphic reactions)
• Heat consumption (heat consumed by endothermic metamorphic reactions, in particular partial melting)