We present wide-field 1.1 mm continuum imaging of the nearby spiral galaxy M 33, conducted with the AzTEC bolometer camera on ASTE. We show that the 1.1 mm flux traces the distribution of dust with T similar to 20K. Combined with far-infrared imaging at 160 mu m, we derived the dust temperature distribution out to a galactic radius of similar to 7 kpc with a spatial resolution of similar to 150 pc. Although the 1.1 mm flux was observed predominantly near star-forming regions, we found a smooth radial temperature gradient declining from similar to 20K to similar to 13 K consistent with recent results from the Herschel satellite. Further comparisons of individual regions show a strong correlation between the cold dust temperature and the K-S band brightness, but not with the ionizing flux. The observed results imply that the dominant heating source of cold dust at few hundred parsec scales is due to non-OB stars, even when associated with star-forming regions.