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With a changing climate, the frequency and intensity of extreme weather events are likely to increase, posing a threat to infrastructure systems' resilience. The response of infrastructure systems to localised failures depends on whether assets are affected randomly, in a targeted strategic way, or any way in between. More than that, infrastructure decisions today, including new routes or improvements to existing assets, will underpin the behaviour of the systems over the next century. It is important to separate and analyse the case of climate-based disruptions and how they affect systems' resilience. This paper presents a probabilistic resilience assessment framework where failure scenarios and network disruptions are generated using weather profile data from climate prediction models with component-level fragility functions. A case study is then carried out to quantify the resilience of Great Britain's railway passenger transport system to high-temperature-related track buckling under the Representative Concentration Pathway 8.5 (RCP8.5) climate change scenario. A 95-year horizon on the resilience of the railway system is drawn. The results also reveal the non-linear responses of the railway system to the increasing temperature and show that models considering random asset failures overestimate the system's resilience.