We present an analysis of the dust and gas in Andromeda, using Herschel images sampling the entire far-infrared peak. We fit a modified-blackbody model to ∼4000 quasi-independent pixels with spatial resolution of 140pc and find that a variable dust-emissivity index (β) is required to fit the data. We find no significant long-wavelength excess above this model, suggesting there is no cold dust component. We show that the gas-to-dust ratio varies radially, increasing from ∼20 in the center to ∼70 in the star-forming ring at 10kpc, consistent with the metallicity gradient. In the 10kpc ring the average β is ∼1.9, in good agreement with values determined for the Milky Way (MW). However, in contrast to the MW, we find significant radial variations in β, which increases from 1.9 at 10kpc to ∼2.5 at a radius of 3.1kpc and then decreases to 1.7 in the center. The dust temperature is fairly constant in the 10kpc ring (ranging from 17 to 20K), but increases strongly in the bulge to ∼30K. Within 3.1kpc we find the dust temperature is highly correlated with the 3.6 μm flux, suggesting the general stellar population in the bulge is the dominant source of dust heating there. At larger radii, there is a weak correlation between the star formation rate and dust temperature. We find no evidence for "dark gas" in M31 in contrast to recent results for the MW. Finally, we obtained an estimate of the CO X-factor by minimizing the dispersion in the gas-to-dust ratio, obtaining a value of (1.9 ± 0.4) × 1020cm-2 [K km s-1]-1. © © 2012. The American Astronomical Society. All rights reserved..