We have computed radiative equilibrium models for the gas in the circumstellar envelope surrounding the hot, classical Be star γ Cassiopeiae. This calculation is performed using a code that incorporates a number of improvements over previous treatments of the disk's thermal structure by Millar & Marlborough and Jones et al.; most importantly, heating and cooling rates are computed with atomic models for H, He, CNO, Mg, Si, Ca, and Fe and their relevant ions. Thus, for the first time, the thermal structure of a Be disk is computed for a gas with a solar chemical composition as opposed to assuming a pure hydrogen envelope. We compare the predicted average disk temperature, the total energy loss in Hα, and the near-IR excess with observations and find that all can be accounted for by a disk that is in vertical hydrostatic equilibrium with a density in the equatorial plane of ρ(R) ≈ (3-5) × 10-11 (R/R*)-2.5 g cm-3. We also discuss the changes in the disk's thermal structure that result from the additional heating and cooling processes available to a gas with a solar chemical composition over those available to a pure hydrogen plasma.