Essentially all low-mass X-ray binaries (LMXBs) in the soft state appear to drive powerful equatorial disc winds. A simple mechanism for driving such outflows involves X-ray heating of the top of the disc atmosphere to the Compton temperature. Beyond the Compton radius, the thermal speed exceeds the escape velocity, and mass loss is inevitable. Here, we present the first coupled radiation-hydrodynamic simulation of such thermally-driven disc winds. The main advance over previous modelling efforts is that the frequency-dependent attenuation of the irradiating SED is taken into account. We can therefore relax the approximation that the wind is optically thin throughout which is unlikely to hold in the crucial acceleration zone of the flow. The main remaining limitations of our simulations are connected to our treatment of optically thick regions. Adopting parameters representative of the wind-driving LMXB GRO~J1655-40, our radiation-hydrodynamic model yields a mass-loss rate that is $simeq5times$ lower than that suggested by pure hydrodynamic, optically thin models. This outflow rate still represents more than twice the accretion rate and agrees well with the mass-loss rate inferred from Chandra/HETG observations of GRO~J1655-40 at a time when the system had a similar luminosity to that adopted in our simulations. The Fe XXV and Fe XXVI Lyman $rm{alpha}~$ absorption line profiles observed in this state are slightly stronger than those predicted by our simulations but the qualitative agreement between observed and simulated outflow properties means that thermal driving is a viable mechanism for powering the disc winds seen in soft-state LMXBs.
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