We present the analysis of the high energy emission of the Galactic black hole binary GX 339-4 in a low/hard state at the beginning of its 2004 outburst . The data from 273 ks of INTEGRAL observations , spread over 4 weeks , are analyzed , along with the existing simultaneous RXTE HEXTE and PCA data . During this period , the flux increases by a factor of \simeq 3 , while the spectral shape is quite unchanged , at least up to 150 keV . The high energy data allows us to detect the presence of a high energy cut-off , generally related to thermal mechanisms , and to estimate the plasma parameters in the framework of the Comptonization models . We found an electron temperature of 60-70 keV , an optical depth around 2.5 , with a rather low reflection factor ( 0.2-0.4 ) . In the last observation , we detected a high energy excess above 200 keV with respect to thermal Comptonization while at lower energy , the spectrum is practically identical to the previous one , taken just 2 days before . This suggests that the low and high energy components have a different origin .