An analytical solution is derived for the transient wall heat conduction problem under arbitrary outdoor air temperature perturbations. This is obtained by expanding the arbitrary perturbation in a Fourier series, consisting of a step function and an infinite sum of cosine and sine functions. The analytical solutions in the cases of step, cosine and sine temperature perturbations are derived separately from each other and are then superimposed to produce the resultant solution. Simple linear expressions are derived, which express the maximum indoor heat flow provoked by the arbitrary temperature perturbation in terms of parameters characterizing the perturbation. Such simple expressions are very useful in air-conditioning calculations for predicting peak loads and sizing heating or cooling equipment.