The electrification of building heating is an effective way to meet the global carbon target. As a clean and sustainable electrified heating technology, air-source heat pumps (ASHPs) are widely used in areas lacking central heating. As a major component of heating systems, heating terminals have great effect on both intermittency and flexibility of the system. In this study, an integrated dynamic model was developed by considering the interaction of thermal processes among building envelopes, terminals, and heat pumps. The radiant heat transfer ratio of the heating terminal, which was introduced in the dynamic thermal balance equations, was a key parameter to describe the characteristic of heat transfer between the terminal and the building. Field tests demonstrated that the simulated results were closer to the tested values when considering the proposed ratio. An intermittent heating control strategy as well as demand response operation were applied to heat pump heating systems respectively. The effect of different terminals on room temperature response speed, energy saving rate, load shifting rate and load shifting efficiency was analysed. The results indicated that heat pumps under intermittent heating were more efficient in buildings with convective heating terminals. Specifically, fan-coil heating systems could use 16.48% less energy, while radiant floor heating systems consumed more energy under intermittent heating. For buildings with convective terminals (such as fan coils), the warm-up time was 0.09 h to 0.33 h, and for those with convective-radiative terminals (such as radiators), the warm-up time was 0.23 h to 4 h under daily intermittent heating, while there was nearly no need to preheat in buildings with radiative terminals (such as radiant floors). On the other hand, the buildings with radiative heating terminals had better flexibility potential. By adopting the model predictive control strategy, the load shifting ratio of radiator heating systems was about 2.9 times that of fan coil heating systems. Finally, an idea of a novel radiation-adjustable heating terminal was proposed in order to achieve both intermittency and flexibility.