While polymers are known as thermal insulators, recent studies show that stretched single chains of polymers have a very high thermal conductivity. In this work, our new simulation scheme for simulation of heat flow in nanoconfined fluids [H. Eslami, L. Mohammadzadeh, and N. Mehdipour, J. Chem. Phys. 135, 064703 (2011)] is employed to study the effect of chain ordering (stretching) on the rate of heat transfer in polyamide-6,6 nanoconfined between graphene surfaces. Our results for the heat flow in the parallel direction (the plane of surfaces) show that the coefficient of thermal conductivity depends on the intersurface distance and is much higher than that of the bulk polymer. A comparison of results in this work with our former findings on the heat flow in the perpendicular direction, with the coefficient of heat conductivity less than the bulk sample, reveal that well-organized polymer layers between the confining surfaces show an anisotropic heat conduction; the heat conduction in the direction parallel to the surfaces is much higher than that in the perpendicular direction. The origin of such anisotropy in nanometric heat flow is shown to be the dramatic anisotropy in chain conformations (chain stretching) beside the confining surfaces. The results indicate that the coefficients of heat conductivity in both directions, normal and parallel to the surfaces, depend on the degree of polymer layering between the surfaces and the pore width.