Dynamic responses and vibration characteristics of a rotating functionally graded material (FGM) beam with a hollow circular cross-section in the temperature field are investigated in this paper. The material properties of the FGM beam are assumed to be temperature-dependent and vary along the thickness direction of the beam. By considering the rigid-flexible coupling effect, the geometrically nonlinear dynamic equations of a hub–FGM beam system are derived by employing the assumed modes method and Lagrange’s equations. With the high-order coupling dynamic model, the effect of temperature variations under two different laws of motion is discussed, and the free vibration of the system is studied based on the first-order approximate coupling model. This research can provide ideas for the design of space thermal protection mechanisms.