A numerical finite-difference approach was used to compute the steady and unsteady flow and heat transfer due to a confined two-dimensional slot jet impinging on an isothermal plate. The jet Reynolds number was varied from Re = 250 to 750 for a Prandtl number of 0.7 and a fixed jet-to-plate spacing of H/W = 5. The flow was found to become unsteady at a Reynolds number between 585 and 610. In the steady regime, the stagnation Nusselt number increased monotonically with Reynolds number, and the distribution of heat transfer in the wall jet region was influenced by flow separation caused by re-entrainment of the spent flow back into the jet. At a supercritical Reynolds number of 750 the flow was unsteady and the net effect in the time mean was that the area-averaged heat transfer coefficient was higher compared to what it would have been in the absence of jet unsteady effects. The unsteady jet exhibited a dominant frequency that corresponded to the formation of shear layer vortices at the jet exit. Asymmetry in the formation of the vortex sheets caused deformation or buckling of the jet that induced a low-frequency lateral jet "flapping" instability. The heat transfer responds to both effects and leads to a broadening of the cooled area.