Well log measurements of compressional and shear velocity (Vp,Vs) 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 (kLAB) measured on the nearly continuous (91% recovery) core. Previous studies have shown the log-derived conductivity (kLOG) to be within ¿15% of kLAB 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 relative large discrepancies between kLOG and kLAB correspond to depths at which laboratory measurements of Vs under in situ conditions deviate from the sonic log Vs. This suggests that sonic log determinations of Vs may not be reliable in dipping, anisotropic rocks. Alternatively, the laboratory Vs 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 Vs measurements, the phonon conduction model may provide a tool for deriving thermal conductivity profiles of the Earth's crust from seismic studies of Vp and Vs. ¿ American Geophysical Union 1993