An equilibrium similarity analysis is applied to the transport equation for <(δθ)2>, the second-order temperature structure function, for decaying homogeneous isotropic turbulence. A possible solution is that the temperature variance <θ2> decays as xn, and that the characteristic length scale, identifiable with the Taylor microscale λ, or equivalently the Corrsin microscale λθ, varies as x1/2. 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 <q2>, viz., <q2>∼xm. Measurements downstream of a grid-heated mandoline combination show that, like <(δq)2>, <(δθ)2> satisfies similarity approximately over a significant range of scales r, when λ, λθ, <q2>, and <θ2> 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 <δu(δq)2> and <δu(δθ)2>, where δu is the longitudinal velocity increment.