Climate change is affecting people’s life worldwide. Not only are extreme events becoming more frequent and destructive, but also a larger variability in meteorological parameters such as temperature, precipitations and wind-speed can be responsible for slow yet irreversible modifications in the natural environment as well as accelerated degradation in materials and structures. In this context, cultural heritage architectural assets can be particularly vulnerable due to the fragility of their material and crucial to be preserved given their historical, artistic and cultural value. For this reason, their preservation needs innovative approaches for analysis and assessment. This paper explores how climate parameters as humidity and temperature affects heritage masonry materials, influencing their mechanical performance. To this aim, multi-physics Finite Element modelling of masonry, including mechanical behaviour and heat-moisture diffusion models in unsaturated porous media, is used to assess how the long-term behaviour in terms of stress state is affected by variation of climatic conditions. Enhanced integration strategies are developed and implemented in Code_Aster software package, showing remarkable accuracy even for larger time steps suitable for analysis of future climate scenarios. The approach is then applied to Durham’s Sandstone, representing the main construction material of the Durham World Heritage Site (WHS), including Durham Castle and Cathedral, representing one of the most significant and pioneering UNESCO World Heritage Sites in the UK. The results under one-year recorded time series of temperature and humidity show a non-negligible influence of environmental conditions to the existing stress in proximity of the exposed surface.