A numerical investigation of two-dimensional (2D) flow inside a rectangular lid-driven cavity (RLDC) is performed, subjected to a vertical temperature gradient. The steady and unsteady nature of the flow in an RLDC is explored by solving the compressible Navier-Stokes equation (NSE) for two Reynolds numbers, Re = 4500 and 5500. In the setup, the bottom wall is heated with respect to the other three sides, which leads to a destabilizing vertical thermal gradient. Thus, there are two forced convection governing the flow: one due to the shearing action of the top lid and the other due to the thermal gradient imposed. The onset and propagation of the instability via the upper right corner of the domain are compared for the two Re considered. These show precessing vortical structures are reminiscent of supercritical flow inside a square lid-driven cavity. A primary core vortex is surrounded by gyrating satellite vortices, which remain in the flow field, even when a saturated state is achieved. Further, we explore the vorticity dynamics with time and the associated spectra, which reinforce the multi-periodic chaotic nature of the flow, irrespective of Re.