The thermal rate constant for a chemical reaction, k(T), can be expressed as the long time limit of the flux-side correlation C-fs(t)=tr[e(-beta(H) over cap /2)(F) over cape(-beta(H) over cap /2)e-(i (H) over capt/(h) over bar)(h) over cape(-i (H) over capt/(h) over bar)]. Previous work has focused on semiclassical (SC) approximations [implemented via an initial value representation (IVR)] for the time evolution operators exp(+/-i (H) over capt/(h) over bar) in the correlation function, and this paper shows how an SC-IVR can also be used to approximate the Boltzmann operators exp(-beta(H) over cap /2). Test calculations show that over a wide temperature range little error is introduced in the rate constant by this SC approximation for the Boltzmann operator.