As sea ice disappears, the emergence of open ocean deep convection in the Arctic has been suggested. Here, using 36 state-of-the-art climate models and up to 50 ensemble members per model, we show that Arctic deep convection is rare even under the strongest warming scenario. Only 5 models have somewhat permanent convection by 2100, while 11 have had convection by the middle of the run. For all, the deepest mixed layers are in the Eurasian basin, by St Anna Trough. When the models convect, that region undergoes a salinification and increasing wind speeds; it is freshening otherwise. We discuss the causality and potential reasons for the opposite trends. Given the model’s different parameterisations, and given that the ensemble members that convect the deepest, most often, are those with the strongest sensitivity, we conclude that differences in deep convection are most likely linked to the model formulation.