The heat pump system employed with a dual evaporator for battery cooling coupled with cabin comfort is an innovative thermal management method. It can be inferred that the refrigerant thermal load distribution can trigger temperature fluctuations for the thermal performance of both battery and cabin. To tradeoff between the thermal management demands of battery and cabin, this study proposed a strategy to promote the decreasing of battery temperature and to ensure battery thermal uniformity with a higher priority. Hence, a transient refrigerant flowrate distribution scheme with a minimum flowrate to satisfy battery thermal demands was researched. According to the proposed method, this study investigated three cases of electric vehicle (EV) acceleration conditions with different driving speed levels. The results indicated that, with the proposed method, the battery module average temperature can be lower than 303 K with a 4–8 K maximum temperature difference. Additionally, the cabin air-supply average temperature would range from 285 K to 287 K, the virtual thermal manikin face and leg temperature range from 296 K to 302 K, and the cabin rear zone temperature ranges from 296 K to 298 K for three acceleration driving conditions. To evaluate the EV cabin thermal comfort, the predicted mean vote (PMV) index was introduced by the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHARE). It also provides evidence that with the proposed method, the thermal comfort in the EV cabin can satisfy the ASHARE proposed value range of ±0.5. The results showed a significant reduction in the temperature fluctuations for cabin thermal comfort and battery thermal management thermal controlling. It offers a satisfactory reference for the refrigerant thermal load distribution strategy applied with the heat pump system connected to the battery and cabin by the dual evaporator.