The anisotropy of small-scale temperature fluctuations in shear flows is analysed by making measurements in high-Reynolds-number atmospheric surface layers. A spherical harmonics representation of the moments of scalar increments is proposed, such that the isotropic part corresponds to the index j = 0 and increasing degrees of anisotropy correspond to increasing j. The parity and angular dependence of the odd moments of the scalar increments show that the moments cannot contain any isotropic part (j = 0), but can be satisfactorily represented by the lowest-order anisotropic term corresponding to j = 1. Thus, the skewnesses of scalar increments (and derivatives) are inherently anisotropic quantities, and are not suitable indicators of the tendency towards isotropy.