An equilibrium similarity analysis is applied to the transport equation for<(δ θ) 2>, the second-order temperature structure function, for decaying homogeneous isotropic turbulence. A possible solution is that the temperature variance< θ 2> decays as x n, and that the characteristic length scale, identifiable with the Taylor microscale λ, or equivalently the Corrsin microscale λ θ, varies as x 1/2. The turbulent Reynolds and Péclet numbers decay as x (m+ 1)/2 when m<− 1, where m is the exponent which characterizes the decay of the turbulent energy< q 2>, viz.,< q 2>∼ x m. Measurements downstream of a grid-heated mandoline combination show that, like<(δ q) 2>,<(δ θ) 2> satisfies similarity approximately over a significant range of scales r, when λ, λ θ,< q 2>, and< θ 2> are used as the normalizing scales. This approximate similarity is exploited to calculate the third-order structure functions. Satisfactory agreement is found between measured and calculated distributions of< δ u (δ q) 2> and< δ u (δ θ) 2>, where δ u is the longitudinal velocity increment.