We report on INTEGRAL observations of the bright black-hole transient GX 339-4 performed during the period August-September 2004. Our data cover three different spectral states, namely Hard/Intermediate State, Soft/Intermediate State and High/Soft State. We investigate the spectral variability of the source across the different spectral states. The hard X-ray spectrum becomes softer during the HIMS-to-SIMS transition, but it hardens when reaching the HSS state. A principal component analysis demonstrates that most of the variability occurs through two independent modes: a pivoting of the spectrum around 6 keV (responsible for 75% of the variance) and an intensity variation of the hard component (responsible for 21%). The pivoting is interpreted as due to changes in the soft cooling photon flux entering the corona, the second mode as fluctuations of the heating rate in the corona. Our spectral analysis of the spectra of GX 339-4 shows a high energy excess with respect to pure thermal Comptonisation models in the HIMS: a non-thermal power-law component seems to be requested by data. In all spectral states joint IBIS, SPI and JEM-X data are well represented by hybrid thermal/non-thermal Comptonisation (EQPAIR). The spectral evolution seems to be predominantly driven by a reduction of the ratio of the electron heating rate to the soft cooling photon flux in the corona, l_h/l_s. The inferred accretion disc soft thermal emission increases by about two orders of magnitude, while the Comptonised luminosity decreases by at most a factor of 3. This confirms that the softening we observed is due to a major increase in the flux of soft cooling photons in the corona associated with a modest reduction of the electron heating rate.
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