Abstract Much research has been focused on maintaining stable humidity conditions in buildings housing heritage collections while reducing energy use. Moisture buffering by collections themselves can have a marked effect on the stabilisation of relative humidity (RH), the key parameter for preservation. Modelling of moisture transport using COMSOL Multiphysics was applied to transform three-dimensional paper and wooden objects into their one-dimensional representations, without changing the moisture uptake and release characteristics. The results were coupled to the modelling of indoor microclimate and energy consumption in collection storage spaces with the use of WUFI ® Plus software. The study revealed the crucial impact of air exchange rate of the building on the stability of indoor RH and the humidification and dehumidification loads required to maintain it. In the adequately air-tight library store, a sizeable paper collection was found to reduce the RH fluctuations from ±9% to ±6% around the yearly average and the energy consumption due to the humidification and dehumidification load by 38% when compared with the empty space, for a high-quality climate control scenario. In turn, a wooden collection, occupying a realistic fraction of a museum store was not large enough to significantly narrow down the RH variations and reduce the energy consumption.