Under the new situation of "coal-to-electricity", the air-source heat pump has become one of the main forms of rural electric heating because of its advantages of safety, economy, high efficiency and cleaning. For the rural air source heat pump-radiator system, a thermal model based on the air source heat pump control principle is deduced, and a multi-objective optimization model for setting the water temperature range of an air-source heat pump with the goals of economy and thermal comfort for electric heating users is established. In addition, based on the traditional Multi-Objective Bacterial Colony Chemotaxis (MOBCC) algorithm, a bacterial individual optimization step time varying strategy and a bacterial colony-oriented mutation strategy are proposed. These improve the convergence and diversity of the solution set. The improved MOBCC algorithm and multi-objective decision-making method based on fuzzy membership function are applied to achieve the optimization. The simulation results of the examples verify the performance of the improved MOBCC algorithm and the correctness of the model. This work is supported by National Natural Science Foundation of China (No. 61873225) and Special Fund for Beijing-Tianjin-Hebei Corporation of Natural Science Foundation of Hebei Province (No. F2016203507).