The effect of wall temperature on the transfer of kinetic energy in a hypersonic turbulent boundary layer for different Mach numbers and wall temperature ratios is studied by direct numerical simulation. A cold wall temperature can enhance the compressibility effect in the near-wall region through increasing the temperature gradient and wall heat flux. It is shown that the cold wall temperature enhances the local reverse transfer of kinetic energy from small scales to large scales, and suppresses the local direct transfer of kinetic energy from large scales to small scales. The average filtered spatial convection and average filtered viscous dissipation are dominant in the near-wall region, while the average subgrid-scale flux of kinetic energy achieves its peak value in the buffer layer. It is found that the wall can suppress the inter-scale transfer of kinetic energy, especially for the situation of a cold wall. A strong local reverse transfer of fluctuating kinetic energy is identified in the buffer layer in the inertial range. Helmholtz decomposition is applied to analyse the compressibility effect on the subgrid-scale flux of kinetic energy. A strong transfer of the solenoidal component of fluctuating kinetic energy is identified in the buffer layer, while a significant transfer of the dilatational component of fluctuating kinetic energy is observed in the near-wall region. It is also shown that compression motions have a major contribution to the direct transfer of fluctuating kinetic energy, while expansion motions play a marked role in the reverse transfer of fluctuating kinetic energy.