We present the numerical study of hydromagnetic (MHD) flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with one wall shrinking and the other at rest in the presence of a transverse applied magnetic field. Different from the classical shooting methodology, we employ a combination of a direct and an iterative method (SOR with optimal relaxation parameter) for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar nonlinear ODEs. Effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigation may be beneficial to the flow and thermal control of polymeric processing.