Grey shaded areas: distribution of temperature as a function of Rosseland optical depth in two representative snapshots of two surface convection simulations of a metal-poor red giant at  [Fe/H]  =  −3. The snapshots were taken 28 h after the start of the simulations. Darker shades indicate temperature values with higher frequency of occurrence. Left panel: temperature distribution from the simulation with self-consistent solution of the radiative transfer equation for a source function with a coherent scattering term (standard case). Continuous blue line: mean temperature stratification from the corresponding simulation assuming a Planckian source function and neglecting the contribution of scattering in optically thin layers, averaged over time and surfaces of constant Rosseland optical depth. Right panel: temperature distribution for the radiative transfer solution assuming a Planckian source function and treating scattering as true absorption everywhere. Continuous red line: corresponding mean temperature stratification. Dashed lines (both panels): mean temperature stratification for the standard-case simulation.