Turbulent mixing and combustion are investigated in a gaseous shear layer formed between two streams: one containing a low concentration of hydrogen in nitrogen and the other containing a low concentration of fluorine in nitrogen. The resulting temperature field is measured simultaneously at eight points across the width of the layer using fast-response cold-wire thermometry. The results show the presence of large, hot structures separated by tongues of cool fluid that enter the layer from either side. The usual bell-shaped mean-temperature profiles therefore result from a duty cycle whereby a fixed probe sees alternating hot and cool fluid, which results in the local mean. The adiabatic flame temperature is not achieved in the mean, at any location across the layer. For fixed velocities, it is found that, in general, two different mean-temperature profiles result from a given pair of reactant compositions if the sides of the layer on which they are carried are exchanged ('flipped'). This finding is a direct consequence of the asymmetric entrainment of fluid into the layer. Results are compared with the predictions of Konrad and discussed in the context of the Broadwell-Breidenthal model. By comparison with the liquid result of Breidenthal, the amount of product formed in the layer at high Reynolds number is found to be dependent upon the Schmidt number. Results for a helium-nitrogen layer are discussed briefly.