In recent experiments, cluster beams of ≳ 100 keV (D2O)+n impacting on deuterated targets produced much higher than expected D – D fusion rates. We present a novel hot plasma shock-wave model for cluster–impact fusion that is capable of explaining and reproducing the known experimental data. We demonstrate that clusters are capable of inducing shock waves, and that concomitant energy losses are negligible in the present experiments. From our model, we present predictions for D – D and D – T fusion rates for a variety of different targets which may give even higher yields in future experiments. Furthermore, we show theoretically that it is highly unlikely that cluster–impact fusion data can be explained on the basis of artifacts such as light ionic contaminants. Finally, we show that the observed line broadening of the proton spectrum is consistent with our prediction of a high temperature in the impact region.