A method is described for the asymptotic study of natural convection problems in the limit of fast flow, when the dimensionless Rayleigh numberRtends to infinity. The Boussinesq approximation is used, and attention is confined to a viscous limit, with the Prandtl number taken as infinite; this makes the fluid momentum negligible. The flow is nevertheless so fast that the temperature is disturbed only in thin layers. The heat equation is studied in these layers, and the effect of the buoyancy in the layers on the motion is expressed in terms of the heat flux.