The large graben-like troughs and smooth plains visible on the surface of Ariel are indicative of a period of high heat flow in the Uranian moon's past. High heat flows on icy moons like Ariel can also enable viscous flow that removes impact crater topography, a process called viscous relaxation. Here we use numerical modeling to investigate the conditions necessary to viscously relax Ariel's largest impact crater, Yangoor, which is 80 km in diameter and unusually shallow. If we assume that Ariel's crust consists of non-porous water ice, heat fluxes ≥60 mW m⁻² are required to reduce an initially deep Yangoor-like crater to its current observed depth. Lower fluxes are required if a high-porosity (30%), low-conductivity surface layer several kilometers thick is assumed to exist, but in any case, fluxes in excess of 30 mW m⁻² are necessary to substantially reduce Yangoor's topography. The inclusion of ammonia dihydrate has a negligible effect on our results despite decreasing the viscosity of Ariel's deep ice. Our results are consistent with previous inferences of high heat fluxes on Ariel, but exceed both expected radiogenic heat fluxes and known equilibrium tidal heat fluxes by an order of magnitude. If Yangoor's shallow depth is the result of tidal heating, then short-lived non-equilibrium tidal dissipation or some other source of energy is required. Notably, although our results do not require the presence of an ocean within Ariel, the thermal conditions necessary to viscously relax Yangoor also imply a relatively thin ice shell (∼10-km thick) if conductive heat transport is assumed.