Given the link between climatic factors on one hand, such as climate change and low frequency climate oscillation indices, and the occurrence and magnitude of heat waves on the other hand, and given the impact of heat waves on mortality, these climatic factors could provide some predictive skill for mortality. We propose a new model, the Mortality-Duration-Frequency (MDF) relationship, to relate the intensity of an extreme summer mortality event to its duration and frequency. The MDF model takes into account the non-stationarities observed in the mortality data through covariates by integrating information concerning climate change through the time trend and climate variability through climate oscillation indices. The proposed approach was applied to all-cause mortality data from 1983 to 2018 in the metropolitan regions of Quebec and Montreal in eastern Canada. In all cases, models introducing covariates lead to a substantial improvement in the goodness-of-fit in comparison to stationary models without covariates. Climate change signal is more important than climate variability signal in explaining maximum summer mortality. However, climate indices successfully explain a part of the interannual variability in the maximum summer mortality. Overall, the best models are obtained with the time trend and the North Atlantic Oscillation (NAO) used as covariates. No country has yet integrated teleconnection information in their heat-health watch and warning systems or adaptation plans. MDF modeling has the potential to be useful to public health managers for the planning and management of health services. It allows predicting future MDF curves for adaptive management using the values of the covariates.