State-of-the-art mobile platforms are powered by heterogeneous system-on-chips that integrate multiple CPU cores, a GPU, and many specialized processors. Competitive performance on these platforms comes at the expense of increased power density due to their small form factor. Consequently, the skin temperature, which can degrade the experience, becomes a limiting factor. Since using a fan is not a viable solution for hand-held devices, there is a strong need for dynamic thermal and power management (DTPM) algorithms that can regulate temperature with minimal performance impact. This paper presents a DTPM algorithm, which uses a practical temperature prediction methodology based on system identification. The proposed algorithm dynamically computes a power budget using the predicted temperature. This budget is used to throttle the frequency and number of cores to avoid temperature violations with minimal impact on the system performance. Our experimental measurements on two different octa-core big.LITTLE processors and common Android applications demonstrate that the proposed technique predicts the temperature with less than 5% error across all benchmarks. Using this prediction, the proposed DTPM algorithm successfully regulates the maximum temperature and decreases the temperature violations by one order of magnitude while also reducing the total power consumption on average by 7% compared with the default solution.