Sleeping is an important method to reduce energy consumption in many information and communication systems. In this paper we focus on a typical server under dynamic load, where entering and leaving sleeping mode incurs an energy and a response time penalty. We seek to understand under what kind of system configuration and control method will sleep mode obtain a Pareto Optimal tradeoff between energy saving and average response time. We prove that the optimal "sleeping" policy has a simple hysteretic structure. Simulation results then show that this policy results in significant energy savings, especially for relatively delay insensitive applications and under low traffic load. However, we demonstrate that seeking the maximum energy saving presents another tradeoff: it drives up the peak temperature in the server, with potential reliability consequences.