The ever-increasing computational demand drives modern electronic devices to integrate more processing elements for pursuing higher computing performance. However, the resulting soaring power density and potential thermal crisis constrain the system performance under a maximally allowed temperature. This paper analytically studies the throughput maximization problem of multi-core platforms under the peak temperature constraints. To take advantage of thermal heterogeneity of different cores for performance improvement, we propose to run each core with multiple speed levels and develop a schedule based on two novel concepts, i.e., the step-up schedule and the m-Oscillating schedule, for multi-core platforms. The proposed methodology can ensure the peak temperature guarantee with a significant improvement in computing throughput up to 89 percent, with an average improvement of 11 percent. Meanwhile, the computational time reduces orders of magnitude compared to the traditional exhaustive search-based approach.