In August 2003, 14,800 heat-related deaths occurred in Paris  during what is considered the warmest summer since at least 1500 , ,  and . These deaths resulted not only from unusually high peak temperatures and a reduction in the diurnal temperature swing, but also from a failure of buildings to successfully modify the external environment. It has been estimated  that by the 2040s, a 2003-type summer is predicted to be average within Europe. Clearly this will have a great impact on morbidity and mortality and produce challenges for emergency services . The effects of climate change on the internal environment are not well known and are the subject of much current research . For building scientists and emergency planners, there is the need to know the general form of the relationship between increases in external temperature due to climate change and increases in internal temperatures. Here we show that the relationship is linear, and that differing architectures give rise to differing constants of proportionality. This is a surprising result as it had been assumed that, given the complexity of the heat flows within large structures, no simple relationship would exist and had not been found in previous work . We term these constants of proportionality climate change amplification coefficients. These coefficients fully describe the change in the internal environment of an architecture given a seasonal or annual change in external climate and can be used to judge the resilience to climate change of a particular structure. The estimation and use of these coefficients for new or existing buildings will allow: the design of more resilient buildings adapted to a changing climate, cost-benefit analysis of refurbishment options and the rational assembly of at-risk registers of vulnerable building occupants.