Proactive content caching at user terminals is studied from an energy efficiency perspective. Assuming that the variable-rate demands of a user can be predicted accurately over a certain time period, the optimal transmission strategy that minimizes the total energy consumption is characterized. The reduction in the energy consumption is obtained both by increasing the total transmission time of a request, and by downloading it at better channel conditions, rather than downloading it at the time of use. Both gains are possible thanks to the limited cache memory at the user device, in which the pre-downloaded content is stored until it is requested by the application layer, such as a video player. We formulate the optimal proactive transmission strategy as the solution of a convex optimization problem, and evaluate the minimum total energy requirement numerically. We also provide a backward water-filling interpretation for the optimal caching strategy.