Assessing climate-driven mortality risk has become an emerging area of research in recent decades. In this paper, we propose a novel approach to explicitly incorporate climate-driven effects into both single- and multi-population stochastic mortality models. The new model consists of two components: a stochastic mortality model, and a distributed lag non-linear model (DLNM). The stochastic component captures the non-climate long-term trend, volatility, and seasonal patterns in mortality rates. The DLNM component captures non-linear and lagged effects of climate variables on mortality, as well as the impact of heat waves and cold waves across different age groups. For model calibration, we propose a novel backfitting algorithm that allows us to disentangle the climate-driven mortality risk from the non-climate-driven stochastic mortality risk. We illustrate the effectiveness and improved short-term (1--18 month) forecasting performance of our model against four alternative models, using data from three European regions: Athens, Lisbon, and Rome. Furthermore, as an application of the proposed modeling framework, we utilize future UTCI data generated from climate models to provide total mortality forecasts into 2045 across these regions under two Representative Concentration Pathway (RCP) scenarios, taking both stochastic mortality improvement trend and climate risk into account. The projections show a noticeable decrease in winter mortality alongside a rise in summer mortality, driven by a general increase in UTCI over time. Although we expect slightly lower overall mortality in the short term under RCP8.5 compared to RCP2.6, a long-term increase in total mortality is anticipated under the RCP8.5 scenario.

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