Transverse injection of a sonic jet array into a hypersonic crossflow constitutes a canonical configuration for film cooling in reusable hypersonic vehicles. Direct numerical simulations are performed at three jet pressure ratios of 5, 10, and 20 (PR5, PR10, and PR20, respectively), to elucidate the mechanisms governing near-wall heat transfer in a hypersonic turbulent boundary layer with jet-array injection. Heat budget analyses quantify the generation and transport of aerodynamic heat. The results reveal that near-wall heat transfer is governed by distinct regional mechanisms. In the upstream interaction region, turbulence amplification within the separation bubble enhances turbulent transport, driving compression and dissipation heat toward the wall and inducing pronounced high heat flux. In the near-wake region, flow induction and turbulence modulation by counter-rotating vortex pairs lead to the formation of streamwise heat-flux streaks. Crucially, a “mean shear–Reynolds stress coupled suppression mechanism” is proposed to explain the sustained heat-flux reduction in the far-wake region. This mechanism arises from the coupling between weakened turbulent momentum transport and delayed velocity-deficit recovery, which maintains a lower near-wall velocity gradient and suppresses mean shear dissipation. Consequently, the wall heat flux is reduced by approximately 34.9%, 46.8%, and 62.6% for PR5, PR10, and PR20, respectively, relative to the baseline turbulent boundary layer. However, a higher pressure ratio reduces the power-normalized heat-reduction efficiency and exacerbates the localized thermal penalty. These findings provide a physical basis for the design and optimization of thermal protection strategies for hypersonic vehicles.