High-definition (HD) maps provide environmental information for autonomous driving systems and are essential for safe planning. While existing methods with single-frame input achieve impressive performance for online vectorized HD map construction, they still struggle with complex scenarios and occlusions. We propose MemFusionMap, a novel temporal fusion model with enhanced temporal reasoning capabilities for online HD map construction. Specifically, we contribute a working memory fusion module that improves the model's memory capacity to reason across a history of frames. We also design a novel temporal overlap heatmap to explicitly inform the model about the temporal overlap information and vehicle trajectory in the Bird's Eye View space. By integrating these two designs, MemFusionMap significantly outperforms existing methods while also maintaining a versatile design for scalability. We conduct extensive evaluation on open-source benchmarks and demonstrate a maximum improvement of 5.4% in mAP over state-of-the-art methods. The project page for MemFusionMap is https://song-jingyu.github.io/MemFusionMap