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The current practice for assessing neonatal postoperative pain relies on bedside caregivers. This practice is subjective, inconsistent, slow, and discontinuous. To develop a reliable medical interpretation, several automated approaches have been proposed to enhance the current practice. These approaches are unimodal and focus mainly on assessing neonatal procedural (acute) pain. As pain is a multimodal emotion that is often expressed through multiple modalities, the multimodal assessment of pain is necessary especially in case of postoperative (acute prolonged) pain. Additionally, spatio-temporal analysis is more stable over time and has been proven to be highly effective at minimizing misclassification errors. In this paper, we present a novel multimodal spatio-temporal approach that integrates visual and vocal signals and uses them for assessing neonatal postoperative pain. We conduct comprehensive experiments to investigate the effectiveness of the proposed approach. We compare the performance of the multimodal and unimodal postoperative pain assessment, and measure the impact of temporal information integration. The experimental results, on a real-world dataset, show that the proposed multimodal spatio-temporal approach achieves the highest AUC (0.87) and accuracy (79%), which are on average 6.67% and 6.33% higher than unimodal approaches. The results also show that the integration of temporal information markedly improves the performance as compared to the non-temporal approach as it captures changes in the pain dynamic. These results demonstrate that the proposed approach can be used as a viable alternative to manual assessment, which would tread a path toward fully automated pain monitoring in clinical settings, point-of-care testing, and homes.