In the framework of the open-time key program "Herschel M 33 extended survey (HerM33es)", we study the far-infrared emission from the nearby spiral galaxy M 33 in order to investigate the physical properties of the dust such as its temperature and luminosity density across the galaxy. Taking advantage of the unique wavelength coverage (100, 160, 250, 350, and 500 μm) of the Herschel Space Observatory and complementing our dataset with Spitzer-IRAC 5.8 and 8 μm and Spitzer-MIPS 24 and 70 μm data, we construct temperature and luminosity density maps by fitting two modified blackbodies of a fixed emissivity index of 1.5. We find that the "cool" dust grains are heated to temperatures of between 11 K and 28 K, with the lowest temperatures being found in the outskirts of the galaxy and the highest ones both at the center and in the bright HII regions. The infrared/submillimeter total luminosity (5-1000 μm) is estimated to be 1.9 × 10 9 +4.0×10 8 −4.4×10 8 L . Fifty-nine percent of the total infrared/submillimeter luminosity of the galaxy is produced by the "cool" dust grains (∼15 K), while the remaining 41% is produced by "warm" dust grains (∼55 K). The ratio of the cool-to-warm dust luminosity is close to unity (within the computed uncertainties), throughout the galaxy, with the luminosity of the cool dust being slightly higher at the center than the outer parts of the galaxy. Decomposing the emission of the dust into two components (one emitted by the diffuse disk of the galaxy and one emitted by the spiral arms), we find that the fraction of the emission from the disk in the mid-infrared (24 μm) is 21%, while it gradually rises up to 57% in the submillimeter (500 μm). We find that the bulk of the luminosity comes from the spiral arm network that produces 70% of the total luminosity of the galaxy with the rest coming from the diffuse dust disk. The "cool" dust inside the disk is heated to temperatures in a narrow range between 18 K and 15 K (going from the center to the outer parts of the galaxy).