Wall time varying conduction heat transfer investigations are very important for the prediction of heating and cooling loads in air conditioning practice and absolutely essential to the passive solar heating design. The walls store heat, absorb and dissipate a fraction of it and transmit the rest into the conditioned space at a later time, which depends on the wall thermal inertia. The present work aims at the description of a developed numerical model, which is validated successfully against analytical results from the literature and allows the prediction of transient and quasi-steady-state thermal behaviour of two basic structural wall design groups of a growing thermal inertia. The model allows the calculation of the time varying conduction heat flux for a wide range of progressively heavier wall designs, under the effect of time varying meteorological conditions, something which allows their design evaluation for a specific application. A drastic reduction of the daily fluctuation of the quasi-steady-state heat flux would be possible by using a broad range of heavier walls, something which can be quantified by the introduction of a dimensionless quantity defined as wall damping-out efficiency. This is attributed to the thermal inertia of a specific wall design, which is also responsible for phasing-out of the maximum heat flux. Both phenomena, which are comparatively investigated for the two groups of specified walls, are desirable particularly for the development of peak load control strategies. (C) 2003 Elsevier B.V All rights reserved.