Nowadays, simulation tools are available for calculating the thermal loads of multiple rooms of buildings, for given inputs. However, due to inaccuracies or uncertainties in some of the input data (e.g., thermal properties, air infiltrations flow rates, building occupancy), the evaluated thermal load may represent no more than just an estimate of the actual thermal load of the spaces. Accordingly, in certain practical situations, simplified methods may offer a more reasonable trade-off between effort and results accuracy than advanced software. Hence, despite the advances in computing power over the last decades, simplified methods for the evaluation of thermal loads are still of great interest nowadays, for both the practicing engineer and the graduating student, since these can be readily implemented or developed in common computational-tools, like a spreadsheet. The method of Mackey and Wright (M&W) is a simplified method that upon values of the decrement factor and time lag of a wall (or roof) estimates the instantaneous rate of heat transfer through its indoor surface. It assumes cyclic behaviour and shows good accuracy when the excitation and response have matching shapes, but it involves non negligible error otherwise, for example, in the case of walls of high thermal inertia. The aim of this study is to develop a simplified procedure that considerably improves the accuracy of the M&W method, particularly for excitations that noticeably depart from the sinusoidal shape, while not introducing a need for an excessive volume of data or complexity in the production of results. In the first simplified procedure discussed in the paper, a full-featured excitation is decomposed into a Fourier series and then the wall's thermal behaviour is reconstructed from the application of the M&W method to each of the N sinusoidal components. Even though this established approach can lead to the most accurate results, given a sufficiently high N, it requires the knowledge of the decrement factor and time lag associated to each component of the Fourier series, which can represent a considerable amount of data. The chief result of the research though is a novel procedure based on a parameter, gamma, that weigh-averages the approximate solution obtained by considering a single term Fourier decomposition of the excitation and the solution by considering the actual excitation. The procedure is more accurate than the original M&W method and will be of interest to researchers with the means of generating values of gamma for the walls which the end users of their research are interested in. It provides promising results for walls ranging from massive to negligible mass. It has been noticed that while using the same values of gamma that had been optimized for the wall facing east, acceptable results are also obtained when altered external excitations are imposed, namely due to intermittency of the direct solar radiation or due to a distinct value of the external heat transfer coefficient. (C) 2015 Elsevier Ltd. All rights reserved.