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High-performance computing data centers have been rapidly growing, both in number and size. Thermal management of data centers can address dominant problems associated with cooling such as the recirculation of hot air from the equipment outlets to their inlets and the appearance of hot spots. In this paper, we show through formalization that minimizing the peak inlet temperature allows for the lowest cooling power needs. Using a low-complexity linear heat recirculation model, we define the problem of minimizing the peak inlet temperature within a data center through task assignment (MPIT-TA), consequently leading to minimal cooling-requirement. We also provide two methods to solve the formulation: Xlnt-GA, which uses a genetic algorithm, and Xlnt-SQP, which uses sequential quadratic programming. Results from small-scale data center simulations show that solving the formulation leads to an inlet temperature distribution that, compared to other approaches, is 2 degC to 5 degC lower and achieves about 20 to 30 percent cooling energy savings at common data center utilization rates. Moreover, our algorithms consistently outperform the minimize heat recirculation algorithm, a recirculation-reducing task placement algorithm in the literature.