Measurements of velocity and temperature fluctuations have been made in flows of air over a strongly heated horizontal surface in conditions of large negative Richardson number and approximating to horizontally homogeneous turbulent flow with constant shear stress and upwards flux of total heat. Within a layer that includes most of the total variation of mean temperature and velocity, the effect of the mean flow on the thermal structure is nearly confined to a change in the length scale which measures the thickness of the viscous-convective layer at the surface but which is also the length scale for the fully turbulent region. Measurements of the mean velocity and the mean-square fluctuation in the stream direction were made for a flow velocity of about 0·70 ms−1 and showed that the profiles of mean temperature and mean velocity are closely similar, implying proportionality at each height of the transfer coefficients for heat and for momentum. The ratio is estimated to be 1·4. The measurements were carried out in conditions such that the Monin-Obukhov length was in the range 8–60 mm and the maximum height of observation was 80 mm.