= Crustal mean temperature from conductive heat flow
{title2=$\overline T_c=T_s+qh_c/(2k)$}
For a crustal layer of thickness $h_c$ with constant <thermal conductivity> $k$, no internal heating and a linear conductive profile, the upward <heat flux> magnitude $q$ obeys <Fourier's law>, $T(z)=T_s+qz/k$ with depth positive downward. Depth averaging gives
$$
\overline T_c=\frac1{h_c}\int_0^{h_c}T(z)\,dz=T_s+\frac{qh_c}{2k}.
$$
The basal excess temperature is $qh_c/k$, twice the mean excess. The formula requires a thickness assumption and a conductive interpretation of the measured flux. Hydrothermal advection, sedimentary thermal effects, internal production and nonlinear conductivity can invalidate a linear extrapolation.
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