We study content caching in a wireless network in which the users are connected through a base station that is equipped with a finite-capacity cache. We assume a fixed set of contents whose popularity varies with time. Users' requests for the content depend on their instantaneous popularity levels. Proactively caching contents at the base station incurs a cost but not having requested contents at the base station also incurs a cost. We propose to proactively cache contents at the base station so as to minimize content missing and caching costs. We formulate the problem as a discounted cost Markov decision problem that is a restless multi-armed bandit problem. We provide conditions under which the problem is indexable and also propose a novel approach to maneuver a few parameters to render the problem indexable. We demonstrate the efficacy of the Whittle index policy via numerical evaluation.

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