Opioid use and overdose have become an important public health issues in the United States. However, understanding the spatial and temporal dynamics of opioid overdose incidents and effects of public health interventions and policy changes can be challenging. Effects may be heterogeneous across space and time, and may exhibit spillover into regions in which the intervention did not take place. Using a publicly available dataset consisting of the time/date, location, and nature of heroin-related emergency calls in the city of Cincinnati, Ohio, we use a Bayesian hierarchical model to characterize and predict the risks of overdose incidents in small areas over time, incorporating geographic, social, and demographic covariates. We characterize the predictive performance of this model, and outline a framework for estimating causal impacts of public health interventions.