Thermal displays have been applied in various haptic applications, from material simulation to interpersonal communication; however, there is insufficient knowledge about the temporal processing in human thermal sense to provide a knowledge basis for thermal display design. In this study, we investigated the physical-perceptual correspondence for dynamic thermal stimulation to shed a light on the temporal processing of human thermal sense. In the experiments, participants reported subjective timings of the temperature onset and temperature peak of continuous temperature changes applied to the thenar eminence. We found that the physical-perceptual correspondence was not consistent for warm and cold stimulations. For warm stimulation, the subjective experience always came after the corresponding physical event. On the other hand, for cold stimulation, while the subjective onset always lagged the physical onset, the subjective temperature peak preceded the physical temperature peak. We analyzed these results in the framework of linear systems theory. The results suggest that the senses of warmth and cold have distinct temporal filtering properties, with the sense of cold being more transient than the sense of warmth. These findings advance our knowledge regarding temporal processing in human thermal sense and serve as a basis for thermal display design.