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In real-time planning, the planner must select the next action within a fixed time bound. Because a complete plan may not have been found, the selected action might not lead to a goal and the agent may need to return to its current state. To preserve completeness, real-time search methods incorporate learning, in which heuristic values are updated. Previous work in real-time search has used table-based heuristics, in which the values of states are updated individually. In this paper, we explore the use of abstraction-based heuristics. By refining the abstraction on-line, we can update the values of multiple states, including ones the agent has not yet generated. We test this idea empirically using Cartesian abstractions in the Fast Downward planner. Results on various benchmarks, including the sliding tile puzzle and several IPC domains, indicate that the approach can improve performance compared to traditional heuristic updating. This work brings abstraction refinement, a powerful technique from offline planning, into the real-time setting.