Previously, our group developed autoregressive (AR) models to predict human core temperature and help prevent hyperthermia (temperature > 39°C). However, the models often yielded delayed predictions, limiting their application as a real-time warning system. To mitigate this problem, here we combined AR-model point estimates with statistically derived prediction intervals (PIs) and assessed the performance of three new alert algorithms [AR model plus PI, median filter of AR model plus PI decisions, and an adaptation of the sequential probability ratio test (SPRT)]. Using field-study data from 22 soldiers, including five subjects who experienced hyperthermia, we assessed the alert algorithms for AR-model prediction windows from 15-30 min. Cross-validation simulations showed that, as the prediction windows increased, improvements in the algorithms' effective prediction horizons were offset by deteriorating accuracy, with a 20-min window providing a reasonable compromise. Model plus PI and SPRT yielded the largest effective prediction horizons (≥18 min), but these were offset by other performance measures. If high sensitivity and a long effective prediction horizon are desired, model plus PI provides the best choice, assuming decision switches can be tolerated. In contrast, if a small number of decision switches are desired, SPRT provides the best compromise as an early warning system of impending heat illnesses.