This article presents a numerical investigation of unsteady laminar mixed convection heat transfer in a two-dimensional square cavity. The cavity is configured such that one of the vertical walls is cooled and slides either with a constant speed or with a sinusoidal oscillation. A portion of the opposite stationery wall is heated by a constant temperature heat source while, the remaining walls of the cavity are thermally insulated. Different configurations of sliding wall movement and a series of Richardson numbers and Strouhal numbers are tested. The results indicate that the direction and magnitude of the sliding wall velocity affect the heat transfer rate. At low Richardson numbers, the average heat transfer rate for the cavity with an oscillating wall is found to be lower compared to that for the cavity with a constant velocity wall. In addition, at a fixed Richardson number, as the Strouhal number decreases the oscillation frequency of average Nusselt number on the vertical walls decreases; however, the oscillation amplitude of average Nusselt number increases.