The temperatures of giant-planet upper atmospheres at mid- to low latitudes are measured to be hundreds of degrees warmer than simulations based on solar heating alone can explain. Modelling studies that focus on additional sources of heating have been unable to resolve this major discrepancy. Equatorward transport of energy from the hot auroral regions was expected to heat the low latitudes, but models have demonstrated that auroral energy is trapped at high latitudes, a consequence of the strong Coriolis forces on rapidly rotating planets. Wave heating, driven from below, represents another potential source of upper-atmospheric heating, though initial calculations have proven inconclusive for Jupiter, largely owing to a lack of observational constraints on wave parameters. Here we report that the upper atmosphere above Jupiter's Great Red Spot - the largest storm in the Solar System - is hundreds of degrees hotter than anywhere else on the planet. This hotspot, by process of elimination, must be heated from below, and this detection is therefore strong evidence for coupling between Jupiter's lower and upper atmospheres, probably the result of upwardly propagating acoustic or gravity waves.