The main purpose of this article is to present the use of the dual reciprocity boundary element method (DRBEM) in the analysis of the unsteady natural convective flow of micropolar fluids in a differentially heated rectangular cavity. The finite-difference method (FDM) is used for time discretization. All the convective terms and vorticity boundary condition are evaluated in terms of DRBEM coordinate matrix. Solutions are obtained for several values of microstructure parameter (k), Rayleigh number (Ra), and aspect ratio (A). Prandtl number values are taken as 0.71 and 7.0. The heat transfer rate (average Nusselt number) of micropolar fluids is found to be smaller than that of Newtonian fluid. Numerical results at steady-state are given in terms of streamlines, isotherms, vorticity contours, and velocity profiles, as well as a table containing Nusselt number values for several Ra and k.