  Dust emission is one of the main windows to the physics of galaxies and to
star formation as the radiation from young, hot stars is absorbed by the dust
and reemitted at longer wavelengths. The recently launched Herschel satellite
now provides a view of dust emission in the far-infrared at an unequaled
resolution and quality up to 500 \mu m. In the context of the Herschel HERM33ES
open time key project, we are studying the moderately inclined Scd local group
galaxy M33 which is located only 840 kpc away. In this article, using Spitzer
and Herschel data ranging from 3.6 \mu m to 500 \mu m, along with HI, H\alpha\
maps, and GALEX ultraviolet data we have studied the emission of the dust at
the high spatial resolution of 150 pc. Combining Spitzer and Herschel bands, we
have provided new, inclination corrected, resolved estimators of the total
infrared brightness and of the star formation rate from any combination of
these bands. The study of the colors of the warm and cold dust populations
shows that the temperature of the former is, at high brightness, dictated by
young massive stars but, at lower brightness, heating is taken over by the
evolved populations. Conversely, the temperature of the cold dust is tightly
driven by the evolved stellar populations.
