We fabricated aggregates of cholesteric cylinders coexisting with the isotropic phase and investigated their dynamics under a temperature gradient. Each constituent cylinder possessed the double-twist (DT) structure, and when a heat flux was applied, the whole aggregates rotated as a rigid-body without changing the DT orientation. The angular velocity was proportional to the heat flux and the rotational direction was determined by the molecular chirality and the flux direction. The result suggests that the rigid-body rotation was driven by the thermomechanical cross-correlation in chiral LCs. We also succeeded in switching the rotation by changing the illumination onto the sample.