© 2013 IEEE. Many of today's data centers experience physical limitations on the power needed to run the data center. The first problem that we study is maximizing the performance (quantified by the reward collected for completing tasks by their individual deadlines) of a data center that is subject to total power consumption (of compute nodes and CRAC units) and thermal constraints. The second problem that we study is how to minimize the power consumption in a data center while guaranteeing that the overall performance does not drop below a specified threshold. For both problems, we develop novel optimization techniques for assigning the performance states of cores at the data center level to optimize the operation of the data center. The resource allocation (assignment) techniques in this paper are thermal aware as they consider effects of performance state assignments on temperature and power consumption by the CRAC units. Our simulation studies show that in some cases our assignment technique achieves about 17% average improvement in the reward collected, and about 9% reduction in power consumption compared to an assignment technique that only considers putting a core in the performance state with the highest performance or turning the core off.