Context. The observed signatures of winds from X-ray binaries are broadly consistent with thermal winds, which are driven by X-ray irradiation of the outer accretion disc. Thermal winds produce mass outflow rates that can exceed the accretion rate in the disc. Aims. We aim to study the impact of thermal wind mass loss on the stability and lightcurves of black hole X-ray binaries subject to the thermal-viscous instability driving their outbursts. Strong mass loss could stop outbursts early, as proposed for the 2015 outburst of V404 Cyg. Methods. We used an analytical model for thermal (Compton) wind mass loss as a function of radius, X-ray spectrum, and luminosity that was calibrated against numerical simulations. We also estimated the fraction of the X-rays, emitted close to the compact object, that are scattered back to the outer disc in the wind. Scattering in the thermal wind couples irradiation to the disc size and inner mass accretion rate. The disc evolution equations were modified to include this wind mass loss and the varying irradiation fraction. Results. Scattering in the strong wind expected of long P_orb systems enhances the irradiation heating of the outer disc, keeping it stable against the thermal-viscous instability. This accounts very well for the existence of persistently bright systems with large discs, such as Cyg X-2, 1E 1740.7−2942, or GRS 1758−258. Mass loss from the thermal wind shortens the outburst, as expected, but it is insufficient in explaining the rapid decay timescale of black-hole X-ray binary outbursts. However, including the wind-related varying irradiation fraction produces lightcurves with plateaus in long P_orb systems like GRO J1655−40. Plateau lightcurves may be a dynamical signature of enhanced irradiation due to scattering in thermal winds. Conclusions. Mass loss due to thermal winds is not a major driver for the outburst dynamics up to luminosities of 0.1 − 0.2 L_Edd. Higher luminosities may produce stronger mass loss but studying them is complicated since the wind becomes opaque. Magnetic winds, which extract angular momentum with little mass loss, seem more promising to explain the fast decay timescales generically seen in black-hole X-ray binaries. Thermal winds can play an important role in the outburst dynamics through the varying irradiation heating. This may be evidenced by relating changes in wind properties, X-ray spectra, or luminosity with changes in the optical emission that traces the outer disc. Simulations should enable more accurate estimates of the dependence of the irradiation onto the disc as a function of irradiation spectrum, radius, and disc wind properties.