The three components of the average temperature dissipation have been measured using a pair of parallel cold wires in an approximately self-preserving turbulent boundary layer. The mean square value of θ,x the temperature derivative in the longitudinal direction, is determined mainly by the use of Taylor's hypothesis, following direct verification of this hypothesis at a few locations in the flow. Mean square values of θ,y and θ,z, the temperature derivatives in directions normal to the flow, were estimated mainly from the curvature of spatial temperature autocorrelations. In the outer layer, the measurements indicate that $\overline{\theta^2}_{,z} > \overline{\theta^2}_{,y} > \overline{\theta^2}_{,x}$, and the resulting distribution for dissipation leads to a good closure of the $\frac{1}{2}\overline{\theta^2}$ budget. In the near-wall region the measurements indicate that $\overline{\theta^2}_{,y} > \overline{\theta^2}_{,z} > \overline{\theta^2}_{,x}$. The ratios $\overline{\theta^2}_{,y}/\overline{\theta^2}_{,x} $ and $\overline{\theta^2}_{,z}/\overline{\theta^2}_{,x}$ are as large as 13 and 7 respectively at y+ = 12, underlining the strong anisotropy in this region. The behaviour of the turbulent diffusion, estimated by difference, provides reasonable support for the accuracy of the near-wall temperature-dissipation measurements. Using existing data of near-wall distributions of the turbulent energy and of its dissipation rate, the timescale for the turbulent-energy dissipation is found to be approximately equal to that for the temperature dissipation.