Abstract The basic equations of laminar compressible flow and heat transfer are applied to the free convection boundary layer along an isothermal plate. Solutions which include the effect of all the parameters involved are given. It is found that in the complete approach, the profiles can not be expressed in terms of one similarity variable and one parameter. The profiles, in dimensionless form, are dependent upon the coordinate along the wall, by means of a compressibility variable suitably defined. In addition to the Prandtl number, two parameters influence the profiles, namely the wall — ambient relative temperature difference and the ratio of specific heats. The effect of the compressibility variable is to increase the heat transfer rate at the wall, for small values of the relative temperature difference, and to decrease it for the large values. The skin friction, however, is always reduced. It is concluded, nevertheless, that as long as the compressibility parameter and the relative temperature difference are not of the same order of magnitude, all such compressibility effects may be neglected. The previous approaches to the free convection problem are shown to be special cases of the general formulation given.