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Total energy minimization in data centers (including both computing and cooling energy) requires modeling the interactions between computing decisions (such as load distribution) and heat transfer in the room, since load acts as heat sources whose distribution in space affects cooling energy. This paper presents the first closed-form analytic optimal solution for load distribution in a machine rack that minimizes the sum of computing and cooling energy. We show that by considering actuation knobs on both computing and cooling sides, it is possible to reduce energy cost comparing to state of the art solutions that do not offer holistic energy optimization. The above can be achieved while meeting both throughput requirements and maximum CPU temperature constraints. Using a thorough evaluation on a real test bed of 20 machines, we demonstrate that our simple model adequately captures the thermal behavior and energy consumption of the system. We further show that our approach saves more energy compared to the state of the art in the field.