We study the wavelength dependence of the dust emission as a function of position and environment across the disk of M33 at a linear resolution of 160 pc using Spitzer and Herschel photometric data. Expressing the emissivity of the dust as a power law, the power-law exponent (beta) is estimated from two independent approaches designed to properly treat the degeneracy between beta and the dust temperature. Both beta and the dust temperature are higher in the inner disk than in the outer disk, contrary to reported beta-T anti-correlations found in other sources. In the cold + warm dust model, the warm component and the ionized gas (Halpha) have a very similar distribution across the galaxy, demonstrating that the model separates the components in an appropriate fashion. The flocculent spiral arms and the dust lanes are evident in the map of the cold component. Both cold and warm dust column densities are high in star forming regions and reach their maxima toward the giant star forming complexes NGC604 and NGC595. beta declines from close to 2 in the center to about 1.3 in the outer disk. beta is positively correlated with star formation and with molecular gas column, as traced by Halpha and CO emission. The lower dust emissivity index in the outer parts of M33 is likely related to the reduced metallicity (different grain composition) and possibly different size distribution. It is not due to the decrease in stellar radiation field or temperature in a simple way because the FIR-bright regions in the outer disk also have a low beta. Like most spirals, M33 has a (decreasing) radial gradient in star formation and molecular-to-atomic gas ratio such that the regions bright in Halpha or CO tend to trace the inner disk, making it difficult to distinguish between their effects on the dust.< Réduire