Heatwave persistence is shaped by processes ranging from large-scale circulation to convection and land-atmosphere interactions. In conventional global climate models, deep convection remains parameterized, whereas storm-resolving simulations explicitly represent more of this variability. How grid spacing and convection treatment affect simulated heatwave persistence, however, remains unclear.</p> <p>We investigate these sensitivities using a hierarchy of atmosphere-only ICON simulations comprising a storm-resolving 2.5 km configuration, two intermediate-resolution 10 km configurations that differ in the treatment of deep convection, and a coarser 40 km configuration with parameterized convection. Heatwave occurrence and persistence, land-atmosphere relationships, post-heatwave precipitation conditions, and blocking-heatwave associations are evaluated against ERA5. All ICON configurations reproduce the broad spatial structure of heatwave occurrence, but agreement with ERA5 does not improve systematically with finer grid spacing and remains strongly region-dependent. Differences are clearer for persistence: ICON-2.5 km overestimates very persistent heatwaves in several regions, with upper-tail exceedance probabilities reaching approximately 40 % above ERA5 in the tropics. The tropical Americas show the strongest sensitivity to convection treatment. There, the 2.5 km and 10 km configurations without parameterized deep convection exhibit positive persistence biases and substantially drier conditions following heatwave termination, whereas configurations with parameterized deep convection are wetter and closer to ERA5. The contrast between the two 10 km simulations shows that convection treatment can strongly affect heatwave persistence even at fixed grid spacing. In the extratropics, where large-scale circulation plays a stronger role, regional heatwave underestimation is more consistently associated with underestimated blocking frequency or a weaker blocking-heatwave relationship.</p> <p>These results show that there is no single mechanism through which finer resolution or more explicit convection modifies heatwaves. Greater process explicitness does not necessarily reduce heatwave biases; instead, changes in convection, precipitation, land-atmosphere coupling, and persistent large-scale atmospheric circulation can reinforce or compensate each other in a regionally dependent manner. Storm-resolving simulations therefore provide important process insights, but improved process representation should not be equated with systematically improved climatological agreement.