The emerging "smart grid" paradigm with associated demand-management programs, such as demand-response (DR), calls for enhanced building energy flexibility. This can be achieved by time-shifting or-shaving building heating and cooling peak loads through the implementation of heating and cooling set-point temperature modulations. However, designing and controlling comfortable DR-induced set-point variations remains a challenge as the psycho-physiology of dynamic thermal perception is still poorly understood. In this paper, we explored the physiological and subjective responses of 29 male and 35 female adults to whole-body warm and cool cyclical thermal conditions and focused on studying the phenomena of "thermal overshoot" and "thermal habituation". We observed that females responded to cooling with a higher rate of cooling of skin temperature and, correspondingly, stronger thermal overshoot responses compared to males. These perceptual differences were explained in terms of skin temperature differences since the relationship between thermal sensation and skin temperature was independent of sex. We tested whether other factors influence the interindividual variability of the sensory response and found that the thermal overshoot response weakens as participants' body mass index increases and their age decreases. Thermal habituation was found to modify skin temperature only after cool exposures. Given that the studied rates of change of the air temperatures are those that can be typically found in buildings during DR events, our results can have implications on the design and control of femaleproofed set-point fluctuations, as designing for an average occupant might result in thermally unacceptable conditions for females.