Exhaust power components due to ELMs, radiation and heat transport across the edge transport barrier (ETB) between ELMs are quantifed for H-mode plasmas in JET-C and JET-ILW for comparison with simulations of pedestal heat transport. In low-current, JET-ILW pulses with a low rate of gas fuelling, the pedestal heat transport is found not to be stiff, i.e. the effective, mean heat diffusivity χ ef f does not increase with the electron temperature gradient dT e /dR ped across the pedestal and the parameter η e = L ne /L Te increases with the conducted loss power across the pedestal, with the latter saturating at mean values η e ped 2. This increase in pedestal temperature gradient is partly due to a relative reduction of the ion neo-classical heat transport (which is more significant at low plasma current) with decreasing collisionality at higher power. In JET-ILW pulses, significantly more power is required at a high gas puffing rate to achieve a similar pedestal pressure and normalised confinement to that in otherwise similar JET-C pulses without gas-puffing. The increased heat transport across the JET-ILW pedestals is caused by changes to the pedestal structure induced by the gas puffing, which is required to mitigate contamination by W impurities sputtered from the target plates. In high-power JET-ILW pulses, the radiated power is dominated by that from W, which exhibits a highly asymmetric poloidal distribution due to toroidal rotation. During the ELMy H-mode phase, the W is concentrated in the outer 'mantle' region (0.7 ≤ ρ N ≤ 0.96) inside the pedestal top by a favourable alignment of profile gradients, where it can be effectively flushed by ELMs. Transport analysis reveals that the strong mantle radiation cools the outer region of the plasma, causing more of the heat to be lost through the electron channel. However, direct cooling by W radiation from the ETB region is shown to be insignificant compared to the power conducted through the pedestal.