Large-scale coherent rolls are observed frequently in unstably stratified turbulent wall-bounded flows where they strongly influence the turbulent transport and the mean flow properties. I will address the question of their genesis by means of a linear stability analysis of the turbulent mean flow where a model of turbulent Reynolds stresses is embedded in the linear stability operator. I will show that the onset of large-scale convection is associated to the linear instability of the mean flow to large-scale streamwise-uniform coherent rolls consistently with the results of recent direct numerical simulations performed in the same setting. I will also discuss the importance of including a model of the Reynolds stresses in the linear operator both in this analysis in resolvent analyses of turbulent shear flows.