Enceladus' cratered terrains contain large numbers of unusually shallow craters consistent with deformation by viscous relaxation of water ice under conditions of elevated heat flow. Here we use high‐resolution topography to measure the relaxation fraction of craters on Enceladus far from the active South Pole. We find that many craters are shallower than expected, with craters as small as 2 km in diameter having relaxation fractions in excess of 90%. These measurements are compared with numerical simulations of crater relaxation to constrain the minimum heat flux required to reproduce these observations. We find that Enceladus' nominal cold surface temperature (70 K) and low surface gravity strongly inhibit viscous relaxation. Under such conditions less than 3% relaxation occurs over 2 Ga even for relatively large craters (diameter 24 km) and high, constant heat fluxes (150 mW m−2). Greater viscous relaxation occurs if the effective temperature at the top of the lithosphere is greater than the surface temperature due to insulating regolith and/or plume material. Even for an effective temperature of 120 K, however, heat fluxes in excess of 150 mW m−2are required to produce the degree of relaxation observed. Simulations of viscous relaxation of Enceladus' largest craters suggest that relaxation is best explained by a relatively short‐lived period of intense heating that decayed quickly. We show that infilling of craters by plume material cannot explain the extremely shallow craters at equatorial and higher northern latitudes. Thus, like Enceladus' tectonic terrains, the cratered regions of Enceladus have experienced periods of extreme heat flux.