The flow and heat transfer characteristics in the jet impingement cooling of a constant heat flux surface have been investigated numerically. Computations are done for vertically downward directed two-dimensional confined slot jets impinging on a constant heat flux surface at the bottom. The principal objective of this study is to investigate the associated heat transfer process in the mixed convection regime. The computed flow patterns and isotherms for various domain aspect ratios and for a range of jet exit Reynolds numbers (100-500) and Richardson numbers (0-10) are analysed to understand the mixed convection heat transfer phenomena. The local and average Nusselt numbers and skin friction coefficients at the hot surface for various conditions are presented. It is observed that for a given domain aspect ratio and Richardson number, the average Nusselt number at the heat flux surface increases with increasing jet exit Reynolds number. On the other hand, for a given aspect ratio and Reynolds number the average Nusselt number does not change significantly with Richardson number indicating that the buoyancy effects are not very significant on the overall heat transfer process for the range of jet Reynolds number considered in this study.