As a measure of energy "quality", exergy is meaningful for comparing the potential for thermal storage. Systems containing the same amount of energy could have considerably different capabilities in matching a demand profile, and exergy measures this difference. Exergy stored in the envelope of buildings is central in sustainability because the environment could be an unlimited source of energy if its interaction with the envelope is optimised for maintaining the indoor conditions within comfort ranges. Since the occurring phenomena are highly fluctuating, a dynamic exergy analysis is required; however, dynamic exergy modelling is complex and has not hitherto been implemented in building simulation tools. Simplified energy and exergy assessments are presented for a case study in which thermal storage determines the performance of seven different wall types for utilising nocturnal ventilation as a passive cooling strategy. Hourly temperatures within the walls are obtained with the ESP-r software in free-floating operation and are used to assess the envelope exergy storage capacity. The results for the most suitable wall types were different between the exergy analysis and the more traditional energy performance indicators. The exergy method is an effective technique for selecting the construction type that results in the most favourable free-floating conditions through the analysed passive strategy.