The Lagrangian temperature anomaly decomposition has emerged as a powerful tool for quantifying the relative importance of adiabatic, advective and diabatic processes during heatwaves. However, its sensitivity to the choice of Lagrangian model, whether pure-trajectory or dispersion-based, remains poorly understood. Using seven different trajectory sets, we apply this decomposition to the June 2021 Pacific Northwest heatwave to examine discrepancies in process attribution across model classes. Pure-trajectory models consistently identify diabatic heating as the dominant contributor, whereas dispersion models attribute the largest fraction to adiabatic warming. A trajectory cluster analysis and parcel position diagnostics reveal that this divergence does not stem from different geographic origins or the near-surface vertical distribution over the target region during the heatwave, which are broadly similar across trajectory sets, but from contrasting vertical histories. While dispersion-model parcels reside at higher altitudes before arrival, exposing them to subsidence warming, pure-trajectory parcels remain near the surface where land–atmosphere feedbacks and antecedent dry soils amplify diabatic heating. These findings demonstrate that this Lagrangian framework is fundamentally sensitive to model choice, particularly to the representation of turbulent motion, which induce parcel vertical dispersion absent in the resolved wind fields. While this study does not establish which Lagrangian model class is most suitable, it represents a first step toward understanding these discrepancies and cautions that heatwave attribution studies relying on a single Lagrangian model should interpret inferred process dominance carefully, as it may reflect methodological choices rather than the underlying physics alone.