The thermal conductivity of two single crystals of potassium (ZK-1, ZK-2) was measured from 2.5\ifmmode^\circ\else\textdegree\fi{} to 40\ifmmode^\circ\else\textdegree\fi{}K. Measurements on a third crystal were made between 10\ifmmode^\circ\else\textdegree\fi{} and 40\ifmmode^\circ\else\textdegree\fi{}K. Additional measurements at 77\ifmmode^\circ\else\textdegree\fi{}K were made on all three crystals. The results are in agreement with the previous measurements of MacDonald, White, and Woods with the exception that the two crystals whose measurements were carried through the conductivity maximum (ZK-1 and ZK-2) exhibited a higher conductivity at the maximum than can be accounted for by electronic conduction. This additional conductivity can be attributed to heat conduction by transverse phonons which, because of the sphericity of the potassium Fermi surface, are not interacting with the free electrons.