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The continuous intersection join query is computationally expensive yet important for various applications on moving objects. No previous study has specifically addressed this query type. We can adopt a naive algorithm or extend an existing technique (TP-Join) to process the query. However, they compute the answer for either too long or too short a time interval, which results in either a very large computation cost per object update or too frequent answer updates, respectively. This motivates us to optimize the query processing in the time dimension. In this study, we achieve this optimization by introducing the new concept of time-constrained (TC) processing. Further, TC processing enables a set of effective improvement techniques on traditional intersection join algorithms. With a thorough experimental study, we show that our algorithm outperforms the best adapted existing solution by several orders of magnitude.