Earth’s magnetic field is generated by turbulent motion in its fluid outer core. Although the bulk of the outer core is vigorously convecting and well mixed, some seismic, geomagnetic and geodynamic evidence suggests that a global stably stratified layer exists at the top of Earth’s core. Such a layer would strongly influence thermal, chemical and momentum exchange across the core–mantle boundary and thus have important implications for the dynamics and evolution of the core. Here we argue that the relevant scenario is not global stratification, but rather regional stratification arising solely from the lateral variations in heat flux at the core–mantle boundary. Using our extensive suite of numerical simulations of the dynamics of the fluid core with heterogeneous core–mantle boundary heat flux, we predict that thermal regional inversion layers extend hundreds of kilometres into the core under anomalously hot regions of the lowermost mantle. Although the majority of the outermost core remains actively convecting, sufficiently large and strong regional inversion layers produce a one-dimensional temperature profile that mimics a globally stratified layer below the core–mantle boundary—an apparent thermal stratification despite the average heat flux across the core–mantle boundary being strongly superadiabatic.