Climate change stands to have a profound impact on human society, and on political and other conflicts in particular. However, the existing literature on understanding the relation between climate change and societal conflicts has often been criticized for using data that suffer from sampling and other biases, often resulting from being too narrowly focused on a small region of space or a small set of events. These studies have likewise been critiqued for not using suitable statistical tools that (i) address spatio-temporal dependencies, (ii) obtain probabilistic uncertainty quantification, and (iii) lead to consistent statistical inferences. In this article, we propose a Bayesian framework to address these challenges. We find that there is a strong and substantial association between temperature anomalies on aggregated material conflicts and verbal conflicts globally. Going deeper, we also find significant evidence to suggest that positive temperature anomalies are associated with social conflict primarily through government-civilian and government-rebel material conflicts, as in civilian protests, rebel attacks against government resources, or acts of state repression. We find that majority of the conflicts associated with climate anomalies are triggered by rebel actors, and others react to such acts of conflict. Our results exhibit considerably nuanced relationships between temperature deviations and social conflicts that have not been noticed in previous studies. Methodologically, the proposed Bayesian framework can help social scientists explore similar domains involving large-scale spatial and temporal dependencies. Our code and a synthetic dataset has been made publicly available.