As the number of data centers increases, it is urgent to reduce their energy consumption. Although servers are becoming more energy-efficient, their idle consumption remains high, which is an issue as data centers are often over-provisioned. This work proposes a novel approach for building data centers with heterogeneous machines carefully chosen for their performance and energy efficiency ratios. We focus on web applications whose load varies over time, and design a scheduler that dynamically reconfigures the infrastructure, by migrating applications and switching machines on or off, so that the energy consumed by the data center is proportional to the load. Experiments evaluate the approach and show the energy savings achieved by our heterogeneous data center design and management while satisfying Quality of Service (QoS) constraints.