Although the relationship between weather and health is widely studied, there are still gaps in this knowledge. The present paper proposes data transformation as a way to address these gaps and discusses four different strategies designed to study particular aspects of a weather-health relationship, including (i) temporally aggregating the series, (ii) decomposing the different time scales of the data by empirical model decomposition, (iii) disaggregating the exposure series by considering the whole daily temperature curve as a single function, and (iv) considering the whole year of data as a single, continuous function. These four strategies allow studying non-conventional aspects of the mortality-temperature relationship by retrieving non-dominant time scale from data and allow to study the impact of the time of occurrence of particular event. A real-world case study of temperature-related cardiovascular mortality in the city of Montreal, Canada illustrates that these strategies can shed new lights on the relationship and outlines their strengths and weaknesses. A cross-validation comparison shows that the flexibility of functional regression used in strategies (iii) and (iv) allows a good fit of temperature-related mortality. These strategies can help understanding more accurately climate-related health.