This paper proposes new solution strategies for a challenging optimization problem, called Cooling-aware Workload Placement Problem, that looks for a workload placement that optimizes the overall data center power consumption given by the sum of the server power consumption and of the computer room air conditioner power consumption. We formulate CWPP as a Mixed Integer Non Linear Problem using a cross-interference matrix that links the workload placement to the cold air temperature. Since state-of-the-art Mixed Integer Non Linear solvers can solve to optimality only the smallest instances, we devised two heuristics to obtain good feasible solutions: (i) a heuristic algorithm based on an integer linear relaxation of the problem, and (ii) a Variable Neighborhood Search algorithm. Both heuristic algorithms are evaluated against the best lower bounds obtained with a Mixed Integer Non Linear solver. Computational results show that both heuristics provide solutions that have a small percentage gap from the optimal solutions.