The Weddell Gyre plays an important role in the global climate system by supplying heat to underneath the ice shelves and in the formation of deep and bottom water masses, which have been subject to widespread warming over past decades. In this study, we investigate the re-distribution of heat throughout the Weddell Gyre by diagnosing the terms of the heat conservation equation for a 1000 m thick layer of water encompassing the core of Warm Deep Water. The spatial distributions of the different advective and diffusive terms in terms of heat tendencies are estimated using gridded climatologies of temperature and velocity, obtained from Argo floats in the Weddell Gyre from 2002 to 2016. While the results are somewhat noisy on the grid scale and the representation of the effects of eddy mixing is highly uncertain due to the need to parameterise them by means of turbulent diffusion, the heat budget (i.e. the sum of all terms) closes (within the uncertainty range) when integrated over the open inflow region in the southern limb, whereas the interior circulation cell remains unbalanced. There is an overall balance in the southern limb between the mean horizontal advection and horizontal turbulent diffusion of heat, whereas the vertical terms contribute comparatively little to the heat budget throughout the Weddell Gyre. Heat convergence due to mean horizontal advection balances with divergence due to horizontal turbulent diffusion in the open southern limb of the Weddell Gyre. In contrast, heat divergence due to mean horizontal advection is much weaker than convergence due to horizontal turbulent diffusion in the interior circulation cell of the Weddell Gyre, due to large values in the latter along the northern boundary due to large meridional temperature gradients. Heat is advected into the Weddell Gyre along the southern limb, some of which is turbulently diffused northwards into the interior circulation cell, while some is likely turbulently diffused southwards towards the shelf seas. This suggests that horizontal turbulent diffusion plays a role in transporting heat both towards the gyre interior where upwelling occurs and towards the ice shelves. Horizontal turbulent diffusion is also a mechanism by which heat can be transported into the Weddell Gyre across the open northern boundary. Temporal deviations from the mean terms are not included due to study limitations. In order to appreciate the role of transient eddying processes, a continued effort to increase the spatial and temporal coverage of observations in the eastern Weddell Sea is required.