In a previous work (Paper I of this series), we presented a procedure for computing the temperature distribution in a stellar atmosphere under the constraint of radiative equilibrium. This scheme, which answers the major requirements of simplicity and computational speed, is based on the choice of proper iteration factors that allow a quick convergence to the correct solution. In this paper, we extended the method to accounting for a stellar atmosphere where convective transport is present. This is achieved by introducing a new iteration factor: the ratio of convective to radiative flux. The new iteration factor is introduced into a new loop of iterations, where the current temperature is doubly corrected by making use of both the convective and the radiative transport equations. Thanks to the use of the radiative iteration factors, as defined in Paper I, also inside the new iteration loop, the computational time of each single iteration is kept small. The introduction of the new factor reduces the number of iterations within the loop to very small proportions.