Abstract: The combustor of a practical oblique-detonation engine requires thermal protection due to the high wall heat flux. Previous studies, mostly focusing on inviscid or viscous adiabatic flow over a wedge, have not clearly elucidated the effects of wall cooling on combustion and flow characteristics within the combustor. In this study, two-dimensional viscous numerical simulations are performed across a range of wedge angles and static pressures to investigate the interaction between an oblique detonation wave (ODW) and a boundary layer developing on either an adiabatic or an isothermal flat plate. The results indicate that as the wall temperature decreases, combustion within the boundary layer is suppressed, the separation region shrinks, and the separation-shock angle increases. Meanwhile, both the skin-friction coefficient and the peak wall pressure increase. At high pressures (high Reynolds numbers), within a limited range of wedge angles, wall cooling can convert a separation-induced oblique detonation into an oblique shock by reducing the effective aerodynamic length of the separation region; whereas at low pressures (low Reynolds numbers), oblique-detonation initiation on the windward side of the separation region is inhibited and the separation length becomes more sensitive to wall temperature. Flow reattachment produces a local heat-flux peak; at high Reynolds numbers, the convective heat-transfer intensity between the separation region and the wall reaches an upper limit. The numerical results are used to recalibrate the classical QP85 correlation between peak heat flux and peak pressure within the separation region, and a power-law scaling for the separation length under cooled-wall conditions is proposed.