Thermosensation is crucial for humans to probe the environment and detect threats arising from noxious heat or cold. Over the last years, EEG frequency-tagging using long-lasting periodic radiant heat stimulation has been proposed as a means to study the cortical processes underlying tonic heat perception. This approach is based on the notion that periodic modulation of a sustained stimulus can elicit synchronized periodic activity in the neuronal populations responding to the stimulus, known as a steady-state response (SSR). In this paper, we extend this approach using a contact thermode to generate both heat- and cold-evoked SSRs. Furthermore, we characterize the temporal dynamics of the elicited responses, relate these dynamics to perception, and assess the effects of displacing the stimulated skin surface to gain insight on the heat- and cold-sensitive afferents conveying these responses. Two experiments were conducted in healthy volunteers. In both experiments, noxious heat and innocuous cool stimuli were applied during 75 seconds to the forearm using a Peltier-based contact thermode, with intensities varying sinusoidally at 0.2 Hz. Displacement of the thermal stimulation on the skin surface was achieved by independently controlling the Peltier elements of the thermal probe. Continuous intensity ratings to sustained heat and cold stimulation were obtained in the first experiment with 14 subjects, and the EEG was recorded in the second experiment on 15 subjects. Both contact heat and cool stimulation elicited periodic EEG responses and percepts. Compared to heat stimulation, the responses to cool stimulation had a lower magnitude and shorter latency. All responses tended to habituate along time, and this response attenuation was most pronounced for cool compared to warm stimulation, and for stimulation delivered using a fixed surface compared to a variable surface.