This paper deals with the free convective air how developing in a vertical channel with a rectangular cross-section heated on one side. The channel geometric and physical properties are such as to simulate an air solar collector suitable for building heating. A calculation method that can be applied to the transient combined heat transfer by conduction through the wall and by convection from the wall to the air stream is presented. The conduction across the wall is computed with a one-dimensional, time-dependent finite difference scheme, with convective boundary conditions at both wall surfaces. For the free convective flow along the channel, the air flow rate and the mean convective coefficient on the heated wall are evaluated by means of suitable correlations. To test the practical applicability of the method, some cases have been calculated and the results are presented. Input data are the internal and external temperatures and the solar power absorbed per unit area as functions of time. The calculation outputs the solar heat gains by convection and conduction and the heat dispersed through the glass. The results show that the method lends itself to a relatively simple application in some realistic cases.