The grating magneto-optical trap (GMOT) requires only one beam and three planar diffraction gratings to form a cloud of cold atoms above the plane of the diffractors. Despite the complicated polarization arrangement, we demonstrate sub-Doppler cooling of Rb-87 atoms to a temperature of 7.6(0.6) mu K through a multistage, far-detuned GMOT in conjunction with optical molasses. A decomposition of the electric field into polarization components for this geometry does not yield a mapping onto standard sub-Doppler laser-cooling configurations. With numerical simulations, we find that the polarization composition of the GMOT optical field, which includes sigma and pi polarized light, does produce sub-Doppler temperatures. (C) 2013 Optical Society of America