Research on the Health effects of temperature has expanded greatly in recent years. mainly (inc to the occurrence of extreme weather events and predicted climate change scenarios. The development of appropriate statistical methodology has been an important component of this research, and standard approaches, primarily based on multi-city time series regression analysis, are now well established. However, particular aspects of temperature-health associations, such as the non-linear and delayed relationship and the joint handling of multi-city data, still pose important niet hodological problems. During my PhD research, I have contributed to the development of statistical methods that, address two particular limitations of traditional approaches, focusing on the development of two modelling frameworks: distributed lag non-linear models and multivariate meta-analysis. The former is a class of models that specify simultaneously non-linear and delayed exposure-response relationships in time series data, while the latter is an extension of traditional metaanalysis for the combination of multiple correlated outcomes across studies, that is also applicable to multi-parameter associations. These methods are placed within the traditional two-stage approach that, is adopted in tcuiperat, ure-health studies. The first stage is city-specific, with analyses deriving the estimated relationship within each city. The second-stage is meta-analytical procedure for combining the results from the first stage. I have implemented these modelling frameworks in two packages within the statistical environment R. In this PhD thesis I present a series of publications which summarize my research work. Their content focuses on three key aspects: the development of the statistical methodology, the implementation of the software, and the application of the methods to real data. The papers are preceded by an epidemiological and statistical introduction to the topic, and followed by u, final discussion where I illustrate potential future developments and provide some conclusions. These methodological advancements contribute several improvements over standard methods that are applied to investigate temperaturehealth associations in tüue series data. and may be easily extended to other research fields 311(1s tudy designs.