Heat supply accounts for a substantial amount of terminal energy usage. However, along with price rises in primary energy, there is an urgent need to reduce the average cost of energy consumption during the purchasing of thermal services. Electric heating, an electricity-fed heating production and delivery technology, has been suggested as a promising method for improving heating efficiency, due to the ease of scheduling. However, the traditional centralized operating methods of electricity purchasing rely on explicit physical modeling of every detail, and accurate future predictions, the implementation of which are rarely practical in reality. To facilitate model-free decisions in the field of electricity purchasing, heat storage, and supply management, aimed at cost saving in a real-time price environment, this study proposes a scheduling framework based on deep reinforcement learning (DRL) and the existence of responsive users. First, the structure of a distributed heating system fed by regenerative electric boilers (REBs), which facilitate shiftable heat-load control, is introduced. A terminal heat demand response model based on thermal sensation vote (TSV), characterizing the consumption flexibility of responsive users, is also proposed. Second, due to thermal system inertia, the sequential decision problem of electric heating load scheduling is transformed into a specific Markov decision process (MDP). Finally, the edge intelligence (EI) deployed on the demand side uses a twin delayed deterministic policy gradient (TD-3) algorithm to address the action space continuity of electric heating devices. The combination of a DRL strategy and the computing power of EI enables real-time optimal scheduling. Unlike the traditional method, the trained intelligent agent makes adaptive control strategies according to the currently observed state space, thus avoiding prediction uncertainty. The simulation results validate that the intelligent agent responds positively to changes in electricity prices and weather conditions, reducing electricity consumption costs while maintaining user comfort. The adaptability and generalization of the proposed approach to different conditions is also demonstrated.