Well log measurements of compressional and shear velocity (V_p, V_s), density, and temperature from the 4 km-deep KTB Vorbohrung (pilot hole) were applied in a phonon conduction model for the thermal conductivity of a crystalline solid. The resulting conductivity estimates were compared with conductivities (k_LAB) measured on the nearly continuous (91% recovery) core. Previous studies have shown the log-derived conductivity (k_LOG) to be within ±15% of k_LAB in isotropic or flat-lying anisotropic crystalline rocks. The section penetrated by the KTB pilot hole includes both predominantly isotropic metabasites and highly anisotropic gneisses with foliation dips ranging from horizontal to vertical. The predictions of the phonon model were accurate within ±4% in the metabasites but inaccurate by as much as 23% in the gneisses. The accuracy of the model in the metabasites confirms the utility of the phonon conduction approach in isotropic or weakly anisotropic rocks, but the discrepancies in the anisotropic gneisses remain unexplained. These relatively large discrepancies between k_LOG and k_LAB correspond to depths at which laboratory measurements of V_s under in situ conditions deviate from the sonic log V_s. This suggests that sonic log determinations of V_s may not be reliable in dipping, anisotropic rocks. Alternatively, the laboratory V_s measurements may not constitute a representative sample, or there may be errors in the phonon conduction model. If the discrepancies can be tied to errors in sonic log V_s measurements, the phonon conduction model may provide a tool for deriving thermal conductivity profiles of the Earth's crust from seismic studies of V_p and V_s.