We map a 50 x 30 area in and around the M17 molecular complex with the French submillimeter balloon-borne telescope PRONAOS, in order to better understand the thermal emission of cosmic dust and the structure of the interstellar medium. The PRONAOS-SPM instrument has an angular resolution of about 3, corresponding to a size of 2 pc at the distance of this complex, and a high sensitivity up to 0.8 MJy/sr. The observations are made in four wide submillimeter bands corresponding to effective wavelengths of 200, 260, 360 and 580 um. Using an improved map-making method for PRONAOS data, we map the M17 complex and faint condensations near the dense warm core. We derive maps of both the dust temperature and the spectral index, which vary over a wide range, from about 10 K to 100 K for the temperature and from about 1 to 2.5 for the spectral index. We show that these parameters are anticorrelated, the cold areas (10-20 K) having a spectral index around 2, whereas the warm areas have a spectral index between 1 and 1.5. We discuss possible causes of this effect, and we propose an explanation involving intrinsic variations of the grain properties. Indeed, to match the observed spectra with two dust components having a spectral index equal to 2 leads to very large and unlikely amounts of cold dust. We also give estimates of the column densities and masses of the studied clumps. Three cold clumps (14-17 K) could be gravitationally unstable.