The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale governing equations, such as the Boltzmann and Navier-Stokes equations, are valid in their respective modeling scales. Without identifying a physical scale between the above two limits for the modeling of the flow motion, it is challenging to develop a multiple scale method to capture non-equilibrium flow physics seamlessly across all regimes. Based on the modeling scale of cell size and implementing conservation laws directly in a discretized space, a well-balanced unified gas-kinetic scheme (UGKS) for multiscale gaseous flow has been constructed and used in the study of non-equilibrium flow and heat transport under external force field. In this paper, static heat conduction problems under external force field in different flow regimes are quantitatively investigated. In the lid-driven cavity case, the stratified flow is observed under external force field. With the increment of external force, the flow topological structure changes dramatically, and the temperature gradient, shearing stress, and external force play different roles in the determination of the total heat flux in different layers corresponding to different flow regimes. As a typical non-Fourier's heat conduction phenomena in the transition regime, the external force enhances the heat flux significantly along the forcing direction, with the relationship (q) over right arrow (force) proportional to(phi) over right arrow, where (q) over right arrow (force) is the force-induced heat flux and 4, is the external force acceleration. This relationship is valid in all flow regimes with non vanishing viscosity coefficient or the limited length of particle mean free path. Both theoretical analysis and numerical experiments are used to show the important role of external force on non-equilibrium heat transfer. (C) 2018 Elsevier Ltd. All rights reserved.