  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.
