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Content caching at the edge of network is a promising technique to alleviate the burden of backhaul networks. In this paper, we consider content caching along time in a base station with limited cache capacity. As the popularity of contents may vary over time, the contents of cache need to be updated accordingly. In addition, a requested content may have a delivery deadline within which the content need to be obtained. Motivated by these, we address optimal scheduling of content caching in a time-slotted system under delivery deadline and cache capacity constraints. The objective is to minimize a cost function that captures the load of backhaul links. For our optimization problem we prove its NP-hardness via a reduction from the Partition problem. For problem solving, via a mathematical reformulation, we develop a solution approach based on repeatedly applying a column generation algorithm and a problem-tailored rounding algorithm. In addition, two greedy algorithms are developed based on existing algorithms from the literature. Finally, we present extensive simulations that verify the effectiveness of our solution approach in obtaining near-to-optimal solutions in comparison to greedy algorithms. The solutions obtained from our solution approach are within 1% from the global optimum.