A rather general formulation is utilized for the stability dependence of the eddy coefficient for heat KH above the lowest 50 m. It contains five empirical parameters which pertain to the magnitude of KH in neutral conditions, its variation with increasing stability, its variation with increasing instability, the extent of a slightly countergradient upward heat flux, and the height variation of KH in stable air above hilly terrain or above a cloud-capped inversion base. The five parameters were evaluated or checked against observations of the thermal modification of polar air moving from New England towards Bermuda, and of the diurnal temperature wave at O'Neill, Nebr. A detailed study of the effects of variation of any of the parameters upon the resultant potential temperature profile is included, as is also the effects of different rates of long-wave radiation, of different cloudiness, and of different large-scale subsidence than those assumed. The empirically obtained formulation for KH giving best agreement has greater stability dependence than that found by previous investigators.