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Unsupervised Domain Adaptation (UDA) has emerged as a powerful solution for the domain shift problem via transferring the knowledge from a labeled source domain to a shifted unlabeled target domain. Despite the prevalence of UDA for visual applications, it remains relatively less explored for time-series applications. In this work, we propose a novel lightweight contrastive domain adaptation framework called CoTMix for time-series data. Unlike existing approaches that either use statistical distances or adversarial techniques, we leverage contrastive learning solely to mitigate the distribution shift across the different domains. Specifically, we propose a novel temporal mixup strategy to generate two intermediate augmented views for the source and target domains. Subsequently, we leverage contrastive learning to maximize the similarity between each domain and its corresponding augmented view. The generated views consider the temporal dynamics of time-series data during the adaptation process while inheriting the semantics among the two domains. Hence, we gradually push both domains towards a common intermediate space, mitigating the distribution shift across them. Extensive experiments conducted on five real-world time-series datasets show that our approach can significantly outperform all state-of-the-art UDA methods. The implementation code of CoTMix is available at \href{https://github.com/emadeldeen24/CoTMix}{github.com/emadeldeen24/CoTMix}.