Blueshifted absorption lines are seen in high inclination black hole binary systems in their disc-dominated states, showing these power an equatorial disc wind. While some contribution from magnetic winds remain a possibility, thermal and thermal- radiative winds are expected to be present. We show results from radiation hydrodynamic simulations that show that the additional radiation force from atomic features (bound-free and lines) is important along with electron scattering. Together, these increase the wind velocity at high inclinations, so that they quantitatively match the observations in H1743-322, unlike purely thermal winds that are too slow. We highlight the role played by shadowing of the outer disc from the (subgrid) inner disc Compton heated layer, and show that the increase in shadow from the higher Compton temperature after the spectral transition to the hard state leads to strong suppression of the wind. Thermal-radiative winds explain all of the spectral features (and their disappearance) in this simplest wind system and magnetic winds play only a minor role. We speculate that thermal-radiative winds can explain all the spectral features seen in the more complex (larger disc size) binaries, GRO J1655-40 and GRS 1915+105, without requiring magnetic winds.