Heat flows up because it is hotter below. q = k × dT/dz — the flow is the gradient times the conductivity — so a high gradient can mean plenty of heat, or it can simply mean poor rock. Only the product is a property of the earth; the gradient on its own is a property of what you happened to drill through.
Straight extrapolation assumes the conductivity and the heat production do not change, which they always do. It is a first estimate and it is usually too hot, because the radiogenic contribution falls off with depth.
A granite is not merely warm because heat passes through it — it makes its own, from uranium, thorium and potassium. Over a few kilometres of thickness that self-heating is a large share of the flow at the surface, and it is why granite terranes are the ones worth drilling.
| rock | heat production µW/m³ |
|---|
A temperature measured at the bottom of a fresh hole is always too cold: the drilling mud cooled the rock and it has not recovered. Take several readings as the hole stands, plot them against the Horner time, and the straight line extrapolates to the temperature the rock actually has.
Heat in place is ρ c V ΔT — how much rock, how hot above the useful limit, and how much heat each cubic metre holds. What can be recovered from it is a much smaller number and a much longer argument.
The uranium and thorium that make the heat are the same ones measured in Radiation and exposure — a granite that warms a district is a granite that needs its radon thought about. Closure temperatures, which turn this gradient into a cooling history, are in Dating a rock.