It has been shown that the energy exchange between two objects can be greatly enhanced when the separation between the objects is on the order of the wavelength of thermal emission. The earliest theoretical and computational work focused on simple planar and spherical geometries, or they resorted to approximations that separated the object to outside of the thermal wavelength \(\lambda_T = hc/(k_BT)\). Since those original works, the study of near-field energy exchange has expanded to object shapes that can be described by a separable coordinate system using a spectral expansion of the dyadic Green function of the system. The boundary element method has also been used to study arbitrary shapes in thermal equilibrium. Application of these new expansion methods to general shapes out of thermal equilibrium will facilitate in the optimization of nanoscale structures. A three step process is used to investigate the effects of object shape on the total and directionality of the energy exchange between objects. First, a general expression for the energy flux between the objects will be formulated. Second, a computational method to evaluate the expression will be implemented. Finally, the effects of varying the surface geometry will be explored. The computational results demonstrate that the total energy exchange between two bodies is influenced by the surface shape of the objects even when the surface areas are held constant. While the primary increase over the classical blackbody energy exchange \(\sigma T^4 A\) is primarily governed by separation of the surfaces, we show that the view factors from classical far-field radiative transfer can be used to predict the change in the total energy exchange from a reference configuration at the same separation when the surface area of the two objects is comparable. Additionally, we demonstrate that the spatial distribution of the energy exchange can be localized into small spatial region with a peak value increased over \SI{30}{\percent} by using two objects with dramatically different projected areas.