There is a remarkable potential for implementing demand response (DR) strategies for several purposes, such as peak load reduction, frequency regulation, etc., by using thermostatically controllable appliances. In this paper, an enduser comfort violation minimization oriented DR strategy for residential heating, ventilation, and air conditioning (HVAC) units is proposed. The proposed approach manipulates the temperature set-point of HVAC thermostats aiming to minimize the average discomfort among end-users enrolled in an DR program, while satisfying the DR event related requirements of the load serving entity. Besides, the fairness of the allocation of the comfort violation among the enrolled end-users is also taken into account. Moreover, maintaining the load factor during the contracted DR period compared to a base case in order to reduce the load rebound effect due to shifting the use of HVAC units is also considered within the proposed strategy. Last but not least, the heat index that considers the impact of humidity is utilized instead of using ambient dry-bulb temperature through a spatio-temporal forecasting approach.