Let us analyse the steady state temperature state of the lithosphere as a function of the thermal conductivity structure. We assume that there is not radioactive heat production. Our simplified model consist of a sedimentary basin that overlies the basement, both of which have a constant conductivity throughout them. Fourier’s law requires that the heat flux in the sediments and the heat flux in the basement is equal at the sediment-basement interface.
The subscripts and refer to sediments and basement respectively. Basement in the current context stands for the entire lithosphere, excluding the sedimentary basin on top. is the conductivity, the thickness, is the surface temperature, is the temperature at the bottom of the lithosphere, and the temperature at the interface between sediments and basement. Solving for yields