This study presents an approach developed to derive a Delayed-Multivariate Exposure-Response Model (D-MERF) useful to assess the short-term influence of temperature on mortality, accounting also for the effect of air pollution (O3 and PM10). By using Distributed, lag non-linear models (DLNM) we explain how city-specific exposure-response functions are derived for the municipality of Rome, which is taken as an example. The steps illustrated can be replicated to other cities while the statistical model presented here can be further extended to other exposure variables. We derive the mortality relative-risk (RR) curve averaged over the period 2004–2015, which accounts for city-specific climate and pollution conditions. Key aspects of customization are as follows: This study reports the steps followed to derive a combined, multivariate exposure-response model aimed at translating climatic and air pollution effects into mortality risk. Integration of climate and air pollution parameters to derive RR values. A specific interest is devoted to the investigation of delayed effects on mortality in the presence of different exposure factors.