Saturn’s moon Enceladus harbours a global subsurface ocean beneath its icy crust. Tidal dissipation within the moon’s core generates a substantial amount of heat which leads to ocean convection. Understanding this transport of mass and heat within the ocean is key to understand exchange processes between core, ocean and ice shell. Previous studies of ocean convection assume oceans of constant thickness and constant superadiabatic temperature gradients between the inner core and outer ice shell. However, observations indicate ocean thickness variations of up to ~20 km from equator to pole and heterogenous tidal dissipation within the core likely results in latitude-dependent temperature gradients. In this study, we analyse how heterogeneities affect circulation patterns and heat transfer in an Enceladan ocean using three-dimensional direct numerical simulations. We focus on a degree-2 meridional thickness profile with varying degree of thermal forcing to analyse the different rotating convection regimes and compare them with those of an ocean of constant thickness. Our results show that the non-uniform ocean gives rise to a latitudinally variable Rayleigh number, causing a potential decoupling of rotating convection regimes experienced locally within the ocean. As in the constant ocean thickness scenario, different regimes of convection exist, which depend on the relative influence of rotation. With increasing thermal forcing, convection moves from being restricted to equatorial regions to filling the whole fluid domain. Heat transport efficiency, as measured by the local Nusselt number, is different for the uniform and non-uniform cases and depends on the convection regime. Nusselt-Rayleigh relations are similar to those obtained for an ocean of uniform thickness, but the relevant Rayleigh number depends on the region of the domain that is convecting.