Blueshifted X-ray absorption lines (preferentially from Fe XXV and Fe XXVI present in the 6-8 keV range) indicating the presence of massive hot disk winds in Black Hole (BH) X-ray binaries (XrB) are most generally observed during the soft states. It has been recently suggested that the non-detection of such hot wind signatures in the hard states could be due to the thermal instability of the wind in the ionisation domain consistent with Fe XXV and Fe XXVI. Studying the wind thermal stability requires however a very good knowledge of the spectral shape of the ionizing Spectral Energy Distribution (SED). We discuss in this paper the expected evolution of the disk wind properties during an entire outburst by using the RXTE observations of GX 339-4 during its 2010-2011 outburst. While GX 339-4 never showed signatures of a hot wind in the X-rays, the dataset used is optimal to illustrate our purposes. We compute the corresponding stability curves of the wind using the SED obtained with the Jet-Emitting Disk model. We show that the disk wind can transit from stable to unstable states for Fe XXV and Fe XXVI ions on a day time scale. While the absence of wind absorption features in hard states could be explained by this instability, their presence in soft states seems to require changes of the wind properties (e.g. density) during the spectral transitions between hard and soft states. We propose that these changes could be partly due to the variation of heating power release at the accretion disk surface through irradiation by the central X-ray source. The evolution of the disk wind properties discussed in this paper could be confirmed through the daily monitoring of the spectral transition of a high-inclination BH XrB.
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