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Spatiotemporal heterogeneity in demand distribution poses a significant challenge for deployment and coverage control in unmanned aerial vehicle (UAV) tasking. Recent disasters such as the January 2025 Los Angeles wildfires have amplified both the urgency and the scale of such UAV operations. Traditional methods typically assume uniform or static demand, overlooking spatial and temporal variations, ultimately leading to suboptimal deployment of UAVs. To address this shortcoming, this paper introduces Spatiotemporal Coverage for Optimal Unmanned Tasking (SCOUT), a method that begins by initially identifying high-demand areas and subsequently refines UAV locations through an iterative, gradient-based update. The resulting deployment and coverage control minimizes a weighted cost function that integrates spatial distances and demand density, thereby enhancing both resource accessibility and equity for the target areas. Evaluation results show that SCOUT consistently outperforms 3D K-means and weighted Voronoi methods. Implementing a continuous deployment task further underscores the strong potential of the method for dynamic decision support in complex and rapidly changing environments.