Driver drowsiness causes fatal driving accidents. Thermal imaging is a suitable drowsiness detection method as it is non-invasive and robust against changes in the ambient light. In this paper, driver drowsiness is detected by measuring the forehead temperature at the region covering the supratrochlear artery and also the cheek temperature. About 30 subjects drove on a highway in a driving simulator in two sessions. A thermal camera was used to monitor the facial temperature pattern. The subjects’ drowsiness levels were estimated by three human observers. The forehead and the cheek regions were located and tracked in each frame. The forehead and the cheek skin temperatures were obtained at three levels of drowsiness. The Support Vector Machine, the K-Nearest Neighbor, and the regression tree classifiers were used. From wakefulness to extreme drowsiness, the forehead skin temperature and the absolute cheek-forehead skin temperature gradient decreased by 0.46°C and 0.81°C, respectively. But the cheek skin temperature increased by 0.35°C in two sessions. The gradient difference is on average 50% higher than the forehead or the cheek temperature change alone. The results indicate that drowsiness can be detected with an accuracy of 82%, sensitivity of 85%, specificity of 90%, and precision of 84%. Driver drowsiness can be detected by monitoring changes in the forehead and the cheek temperature signal. Also, the temperature gradient can be used as a more robust and sensitive indicator of drowsiness.