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Data center operators generally overprovision IT and cooling capacities to address unexpected utilization increases that can violate service quality commitments. This results in energy wastage. To reduce this wastage, we introduce HCP (Holistic Capacity Provisioner), a service latency aware management system for dynamically provisioning the server and cooling capacity. Short-term load prediction is used to adjust the online server capacity to concentrate the workload onto the smallest possible set of online servers. Idling servers are completely turned off based on a separate long-term utilization predictor. HCP targets data centers that use chilled air cooling and varies the cooling provided commensurately, using adjustable aperture tiles and speed control of the blower fans in the air handler. An HCP prototype supporting a server heterogeneity is evaluated with real-world workload traces/requests and realizes up to 32% total energy savings while limiting the 99th-percentile and average latency increases to at most 6.67% and 3.24%, respectively, against a baseline system where all servers are kept online.