A number of X-ray binaries exhibit clear evidence for the presence of disk winds in the high/soft state. A promising driving mechanism for these outflows is mass loss driven by the thermal expansion of X-ray heated material in the outer disk atmosphere. Higginbottom \& Proga recently demonstrated that the properties of thermally-driven winds depend critically on the shape of the thermal equilibrium curve, since this determines the thermal stability of the irradiated material. For a given spectral energy distribution, the thermal equilibrium curve depends on exact balance between the various heating and cooling mechanisms at work. Most previous work on thermally-driven disk winds relied an analytical approximation to these rates. Here, we use the photoionization code \textsc{cloudy} to generate realistic heating and cooling rates which we then use in a 2.5D hydrodynamic model computed in ZEUS to simulate thermal winds in a typical black-hole X-ray binary. We find that these heating and cooling rates produce a significantly more complex thermal equilibrium curve, with dramatically different stability properties. The resulting flow, calculated in the optically thin limit, is qualitatively different from flows calculated using approximate analytical rates. Specifically, our thermal disk wind is much denser and slower, with a mass-loss rate that is a factor of two higher and characteristic velocities that are a factor of three lower. The low velocity of the flow -- $v_{max} ≃ 200$~km~s$^{-1}$ -- may be difficult to reconcile with observations. However, the high mass-loss rate -- 15$\times$ the accretion rate -- is promising, since it has the potential to destabilize the disk. Thermally-driven disk winds may therefore provide a mechanism for state changes. ; Comment: 10 Page, 8 figures, Accepted for publication in ApJ