Individual lava flows in flood basalt provinces are composed of sheet pāhoehoe lobes and the 10-100 m thick lobes are thought to form by inflation. Quantifying the emplacement history of these lobes can help infer the magnitude and temporal dynamics of these prehistoric eruptions. Here we use a phase-field model to describe solidification and re-melting of sequentially-emplaced lava flows to explore additional processes that may lead to thick flows. We calibrate model parameters using field measurements at Makaopuhi lava lake. We vary the thickness of individual flows and the time interval between eruptions to study the interplay between thermal evolution, flow thickness and emplacement frequency. Our theoretical analysis shows that, if the time between emplacement is sufficiently short, reheating and re-melting may merge sequentially emplaced flows — making flows appear thicker than they actually were. Our results suggest that fused flows could be another mechanism that creates apparently thick lava flows.