Topology optimization design of cold plate flow channels is a potential approach to improve the performance of battery thermal management systems. In this paper, four objective functions, such as maximum heat exchange, maximum outlet enthalpy, minimum solid domain temperature, and multi-objective function, are used to investigate the effect of the objective function on the topology optimization flow channel shape and cooling performance. The results show that the cold plate channel shape can be adjusted according to the objective function. With the inlet flow rate of 0.002 kg·s−1, the inlet coolant temperature of 25 °C, the ambient temperature of 20 °C, and the 3C-rate discharge, it was found that the topology optimization cold plate with maximum outlet enthalpy as an objective function will give the best cooling performance, in which the maximum temperature of the battery is 29.65 °C, which is 0.48 °C less than the battery with convectional rectangular channel cold plate cooling. For the multi-objective function, the increase in the weighting coefficient of the heat transfer term can improve the cooling capacity of the cold plate, and the increase in the weighting coefficient of the flow term can reduce the flow resistance of the cold plate and enhance the efficiency of energy utilization. In addition, the unsteady battery temperature is calculated during the entire 3C-rate discharge process, and it is found that the topology optimization cold plate can slow down the increase of battery temperature and improve the proportion of battery discharge time at ideal temperature.