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Description: Meridional atmospheric heat transport (AHT) has been investigated through three broad perspectives: dynamic perspective, linking AHT to the poleward flux of moist static energy (MSE) by atmospheric motions; an energetic perspective, linking AHT to energy input to the atmosphere by top-of-atmosphere radiation and surface heat fluxes; and a diffusive perspective, representing AHT in terms down-gradient energy transport. It is shown here that the three perspectives provide complementary diagnostics of meridional AHT and its changes under greenhouse-gas forcing. When combined, the energetic and diffusive perspectives offer prognostic insights: anomalous AHT is constrained to satisfy the net energetic demands of radiative forcing, radiative feedbacks, and ocean heat uptake; in turn, the meridional pattern of warming must adjust to produce those AHT changes, and does so approximately according to diffusion of anomalous MSE. The relationship between temperature and MSE exerts strong constraints on the warming pattern, favoring polar amplification. These conclusions are supported by use of a diffusive moist energy balance model (EBM) that accurately predicts zonal-mean warming and AHT changes within comprehensive general circulation models (GCMs). A dry diffusive EBM predicts similar AHT changes in order to satisfy the same energetic constraints, but does so through tropically-amplified warming -- at odds with the GCMs' polar-amplified warming pattern. The results suggest that polar-amplified warming is a near-inevitable consequence of a moist, diffusive atmosphere's response to greenhouse-gas forcing. In this view, atmospheric circulations must act to satisfy net AHT as constrained by energetics.