In this article, a comprehensive numerical study of MHD axisymmetric stagnation point flow with radiation effects towards a heated shrinking sheet immersed in an electrically conducting incompressible viscous fluid in the presence of a transverse magnetic field is analyzed. The governing continuity, momentum, and heat equations together with the associated boundary conditions are first transformed to a set of self-similar nonlinear ordinary differential equations and are then solved by a method based on finite difference discretization. Some significant features of the flow and heat transfer in terms of normal and horizontal velocities and temperature field for various values of the governing parameters are analyzed, discussed, and presented through tables and graphs. The present investigations predict that the shear stresses increase and the thermal boundary layer becomes thinner by applying a strong magnetic field. The heat loss per unit area from the sheet decreases with an increase in the shrinking parameter. The thermal boundary layer thickness decreases with increasing values of the radiation parameter. The present results may be beneficial in flow and thermal control of polymeric processing.