  The Andromeda Galaxy (M31) is one of a few galaxies that has sufficient
angular size on the sky to be resolved by the Planck satellite. Planck has
detected M31 in all of its frequency bands, and has mapped out the dust
emission with the High Frequency Instrument, clearly resolving multiple spiral
arms and sub-features. We examine the morphology of this long-wavelength dust
emission as seen by Planck, including a study of its outermost spiral arms, and
investigate the dust heating mechanism across M31. We find that dust dominating
the longer wavelength emission ($\gtrsim 0.3\,$mm) is heated by the diffuse
stellar population (as traced by 3.6$\,\mu$m emission), with the dust
dominating the shorter wavelength emission heated by a mix of the old stellar
population and star-forming regions (as traced by 24$\,\mu$m emission). We also
fit spectral energy distributions (SEDs) for individual 5' pixels and quantify
the dust properties across the galaxy, taking into account these different
heating mechanisms, finding that there is a linear decrease in temperature with
galactocentric distance for dust heated by the old stellar population, as would
be expected, with temperatures ranging from around 22$\,$K in the nucleus to
14$\,$K outside of the 10$\,$kpc ring. Finally, we measure the integrated
spectrum of the whole galaxy, which we find to be well-fitted with a global
dust temperature of ($18.2\pm1.0$)$\,$K with a spectral index of $1.62\pm0.11$
(assuming a single modified blackbody), and a significant amount of free-free
emission at intermediate frequencies of 20-60$\,$GHz, which corresponds to a
star formation rate of around $0.12$M$_\odot\,$yr$^{-1}$. We find a
$2.3\,\sigma$ detection of the presence of spinning dust emission, with a
30$\,$GHz amplitude of $0.7\pm0.3\,$Jy, which is in line with expectations from
our Galaxy.
