This study compares and contrasts the ability of three different mathematical modeling techniques to predict individual-specific body core temperature variations during physical activity. The techniques include a first-principles, physiology-based (SCENARIO) model, a purely data-driven model, and a hybrid model that combines first-principles and data-driven components to provide an early, short-term (20-30 min ahead) warning of an impending heat injury. Their performance is investigated using two distinct datasets, a Field study and a Laboratory study. The results indicate that, for up to a 30 min prediction horizon, the purely data-driven model is the most accurate technique, followed by the hybrid. For this prediction horizon, the first-principles SCENARIO model produces root mean square prediction errors that are twice as large as those obtained with the other two techniques. Another important finding is that, if properly regularized and developed with representative data, data-driven and hybrid models can be made "portable" from individual to individual and across studies, thus significantly reducing the need for collecting developmental data and constructing and tuning individual-specific models.