By performing 3D simulations of thermal convection and tidal dissipation, we investigated the effect of tidal heating on the onset of convection in Enceladus’s ice shell. We considered a composite non-Newtonian rheology including diffusion, grain-size-sensitive and dislocation creeps, and we defined an effective tidal viscosity reproducing the dissipation function as predicted by the Andrade rheology. For simulations with no or moderate tidal heating, the onset of convection requires ice grain sizes smaller than or equal to 0.5-0.6 mm. For simulations including significant tidal heating (>10-6 W m-3), the critical grain size for the onset of convection is shifted up to values of 1-1.5 mm. Whatever the width of the internal ocean, convection is initiated in the polar region due to enhanced tidal dissipation at high latitudes. For a given eccentricity value, the onset of convection depends on the ocean width, as tidal flexing and hence tidal heat production is controlled by the ocean width. For heating rates larger than 5-9 × 10-7 W m-3, we systematically observe the occurrence of melting in our simulations, whatever the grain size and for both convecting and non-convecting cases. Grain sizes smaller than 1.5 mm, required to initiate convection, may be obtained either by the presence of a few percent of impurities limiting the grain growth by pinning effects or by the increase of stress and hence dynamic recrystallization associated with tidally-induced melting events.