In the context of climate change, understanding and modeling temperature anomalies has become increasingly crucial. This study proposes an approach that combines Integrated Nested Laplace Approximations (INLA) and Stochastic Partial Differential Equations (SPDE) to analyze the spatio-temporal dynamics of temperature anomalies on a global scale. Using ERA5 data from the Copernicus Data Store, we examine temperature anomalies worldwide. Our methodology integrates spatial modeling with extreme value theory, enabling a detailed characterization of both spatial and temporal dependencies. Temperature anomalies are defined by threshold exceedances and analyzed using advanced statistical techniques. First-order statistical characteristics, such as the intensity function, are estimated to assess the multi-scale structures of these anomalies. This approach offers promising prospects for analyzing global climate risks and assessing the impacts of climate change. The findings could improve the modeling of climate risks by providing a robust statistical framework to quantify dependencies between temperature anomalies, thus enhancing risk assessments and informing climate adaptation strategies.