The influence of the atmospheric boundary layer (ABL) stability on dust emitted from saltation is usually neglected. This has been challenged by two recent studies which suggested a dependency of the dust emission flux particle size distribution (PSD) to the thermal stratification. Both studies observed a dust flux enrichment in fine particles with instability but for two different explanations: (a) a larger eddy diffusivity of submicron particles with instability, and (b) an enhanced turbulence and friction velocity u* stochasticity with instability, increasing saltation bombardment and fine-dust emission. Here, we discuss and investigate these two propositions using the WIND-O-V (WIND erOsion in presence of sparse Vegetation's) 2017 data set. We first show that the first explanation and the observed stability effect on the dust flux are questionable. We, then, investigate the second explanation in the context of the enhanced influence of ABL-scale motions on the near-surface turbulence and u* stochasticity with increasing instability. This second explanation appears only possible at the transition between windy and free convection regimes where u* is close to its erosion threshold value. However, this intermediate regime appears more convective than the erosion event from whom the second explanation was proposed. Overall, our results show no thermal stability effect on the dust emission flux PSD. Instead, u* and the air relative humidity seem to be the main meteorological variables influencing the dust emission flux PSD. We, in particular, suggest that the air relative humidity may have affected the surface soil moisture, and thus the interparticle cohesion, through water vapor adsorption.Read less <