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A strong heat load in buildings and cities during the summer is not a new phenomenon. However, prolonged heat waves and increasing urbanization are intensifying the heat island effect in our cities; hence, the heat exposure in residential buildings. The thermophysiological load in the interior and exterior environments can be reduced in the medium and long term, through urban planning and building physics measures. In the short term, an increasingly vulnerable population must be effectively informed of an impending heat wave. Building simulation models can be favorably used to evaluate indoor heat stress. This study presents a generic simulation model, developed from monitoring data in urban multi-unit residential buildings during a summer period and using statistical methods. The model determines both the average room temperature and its deviations and, thus, consists of three sub-models: cool, average, and warm building types. The simulation model is based on the same mathematical algorithm, whereas each building type is described by a specific data set, concerning its building physical parameters and user behavior, respectively. The generic building model may be used in urban climate analyses with many individual buildings distributed across the city or in heat–health warning systems, with different building and user types distributed across a region. An urban climate analysis (with weather data from a database) may evaluate local differences in urban and indoor climate, whereas heat–health warning systems (driven by a weather forecast) obtain additional information on indoor heat stress and its expected deviations.