A thermal flutter criterion is developed in this paper for a space structure with flexible appendages, considering the coupling between the hub and the appendage with a tip mass. The validity of this criterion is demonstrated by finite element simulations. This criterion clarifies the impact of the mass characteristics of the flexible appendage and the hub on the stability of the thermally induced vibration. In addition, this criterion can degenerate to the existing criterion with cantilever flexible appendages when the mass characteristics of the hub are much larger than those of the flexible appendage.