Wall temperature is a crucial factor for the transition of hypersonic boundary layers. This paper investigates the wall temperature effects on the hypersonic boundary-layer transition over an inclined blunt cone with two wall temperatures by direct numerical simulations and instability analysis. The breakdown processes of leeward streamwise vortices and crossflow vortices are both studied. Inner modes with lower phase velocities and outer modes with higher phase velocities are responsible for the breakdown of leeward streamwise vortices respectively in cooled- and heated-wall cases. A higher wall temperature will promote the boundary layer transition in the vicinity of the leeward centerline due to the collision of nearby crossflow vortices with the leeward mushroom structure, instead of by destabilizing inner and outer modes. In the crossflow-dominated region, the transition is triggered by the interaction between second modes and crossflow vortices for the cooled-wall case. Increasing the wall temperature will promote the transition in this region even though second modes are suppressed.