This paper deals with the prediction of body core temperature during physical activity in different environmental conditions using first-principles models and data-driven models. We argue that prediction of physiological variables through other correlated physiological variables using data-driven techniques is an ill-posed problem. To make predictions produced by data-driven models accurate and stable they need to be regularized. We demonstrate on data collected during laboratory study that data-driven models, if regularized properly, can outperform first-principles models in terms of accuracy of core temperature predictions. We also show that data-driven models can be made "portable" from one subject to another, thus, making them a valuable, practical tool when data from only one subject is available to "train" the model.