Although heat waves are one of the most dangerous types of weather-related hazards, their underlying mechanisms are not yet sufficiently understood. Especially, there is still no scientific consensus about the relative importance of the three key processes: horizontal temperature transport, subsidence accompanied by adiabatic heating, and diabatic heating. The current study quantifies these processes using a Eulerian method based on tracer advection, which allows one to extract Lagrangian information. For each grid point at any time, the method yields a decomposition of temperature anomalies into the aforementioned processes, complemented by the contribution of a pre-existing anomaly. Two different approaches for this decomposition are employed. The first approach is based on full (absolute) fields of the respective terms, whereas the second approach is based on anomaly fields of the respective terms, i.e., deviations from their corresponding climatologies. The two approaches offer two distinct perspectives on the same subject matter. By analyzing two recent heat waves, it is shown that the two decompositions yield substantial differences regarding the relative importance of the processes. A statistical analysis indicates that these differences are not coincidental, but characteristic for the respective regions. It is concluded that the Lagrangian characterization of heat waves is a matter of perspective.