Data centers, as the infrastructure of all information services, cost tremendous amount of energy. Reducing the hot spot temperature in the data center room is benefit to prevent overheating of devices, and to increase cooling system efficiency. In this paper, we study the problem of optimal power distribution among racks for minimal hot spot temperature. The temperature rise matrix (TRM) model is used for the purpose of fast estimation of the thermal environment. The accuracy of the model is evaluated by conducting numerical simulations of computational fluid dynamics (CFD). Using the TRM model, optimal distributing of heating power is converted into a linear programming problem, which can be solved by highly efficient algorithms, such as Simplex. Furthermore, with realistic constraints including rack idle power and power upper limit, an iteration method is proposed to calculate the optimal power distribution along with the optimal on/off states of the racks. Obtained solutions are discussed and validated by comparing with CFD simulations. Results show that the TRM model is acceptable in evaluating temperature rises in the forced-convection-dominated scenarios, and the proposed method is able to obtain optimal power distributions under various levels of total power demand.