An analysis of Hα and Hβ spectra in a sample of 30 cool dwarf and subgiant stars is presented using MARCS model atmospheres based on the most recent calculations of the line opacities. A detailed quantitative comparison of the solar flux spectra with model spectra shows that Balmer line profile shapes, and therefore the temperature structure in the line formation region, are best represented under the mixing length theory by any combination of a low mixing-length parameter α and a low convective structure parameter y. A slightly lower effective temperature is obtained for the sun than the accepted value, which we attribute to errors in models and line opacities. The programme stars span temperatures from 4800 to 7100 K and include a small n...