This paper proposes a distributed cluster control strategy for thermostatically controlled loads (TCLs) to enable precise tracking of the reference power by the aggregated TCL cluster. The proposed strategy takes into account temperature-based priority to ensure fair scheduling among TCLs. Besides, as priorities tend to equalize across all TCLs after multiple control periods, a sub-cluster splitting strategy is introduced to enhance power tracking accuracy. The proposed strategy operates in a distributed manner, significantly reducing the aggregator's resource consumption in communication and computation. Furthermore, it employs asynchronous communication, making it suitable for practical implementation. Simulation results demonstrate that the proposed method can realize the accurate tracking of TCLs cluster aggregated power to the reference power.