The thermoelectric (TE) properties of a material are dramatically altered when electron-electron interactions become the dominant scattering mechanism. In the degenerate hydrodynamic regime, the thermal conductivity is reduced and becomes a decreasing function of the electronic temperature, due to a violation of the Wiedemann-Franz law. We here show how this peculiar temperature dependence gives rise to new striking TE phenomena. These include an 80-fold increase in TE efficiency compared to the Wiedemann-Franz regime, dramatic qualitative changes in the steady state temperature profile, and an anomalously large Thomson effect. In graphene, which we pay special attention to here, these effects are further amplified due to a doubling of the thermopower.