Frictional heat generates at frictional surface caused by contact between bristles of brush seal and rotor, which leads to early failure of the seal, especially downstream stage of multi-stage brush seal (MBS). In this paper, a three-dimensional tube bundle model of the MBS was established to study change of heat flux on the frictional surface among stages, internal temperature distribution of bristles and leakage flow characteristics of the seal. Moreover, three control strategies (i.e., increasing height of backing plate to rotor hbp, decreasing interference between bristles and rotor Δr and decreasing axial width of bristle pack wab) were analyzed to further investigate influence mechanism of the frictional heat. Results showed that the frictional heat at bristle tips mainly depend on formation of frictional heat caused by friction between bristle tip and rotor, transfer of heat from upstream stage to downstream one and dissipation of heat with flow of the airflow passing through the seal. For a traditional MBS with same structural single-stage seal units, a remarkable increasing bristle temperature at bristle tip of downstream stage and an increasing vortex area of airflow with higher temperature in chambers implied accumulation of the frictional heat at the downstream stages. Increase of hbp enhanced dissipation of the heat due to increasing passage area of airflow. Both decrease of Δr and decrease of wab obviously reduced bristle temperatures at downstream stages due to decreasing formation of the frictional heat. Furthermore, the decrease of wab had a lower bristle temperature compared to the increase of hbp, indicating a higher impact of the frictional heat formation on bristle temperature at downstage stages.