  The integrated Spectral Energy Distributions of the Large and Small
Magellanic Cloud appear significantly flatter than expected from dust models
based on their FIR and radio emission. The origin of this millimetre excess is
still unexplained, and is here investigated using the Planck data. The
background CMB contribution is subtracted using an ILC method performed locally
around the galaxies. The foreground emission from the Milky Way is subtracted.
After subtraction, the emission of both galaxies correlates closely with the
gas emission of the LMC and SMC. The millimetre excess in the LMC can be
explained by CMB fluctuations, but a significant excess is still present in the
SMC SED. The Planck and IRIS data at 100 micron are combined to produce thermal
dust temperature and optical depth maps of the two galaxies. The LMC
temperature map shows the presence of a warm inner arm already found with the
Spitzer data, but also shows the existence of a previously unidentified cold
outer arm. Several cold regions are found along this arm, some of which are
associated with known molecular clouds. The average emissivity spectral index
is found to be consistent with beta=1.5 and beta=1.2 below 500 microns for the
LMC and SMC respectively, significantly flatter than the values observed in the
Milky Way. Furthermore, there is evidence in the SMC for a further flattening
of the SED in the sub-mm. The spatial distribution of the millimetre dust
excess in the SMC follows the gas and thermal dust distribution. Different
models are explored in order to fit the dust emission in the SMC. It is
concluded that the millimetre excess is unlikely to be caused by very cold dust
emission and that it could be due to a combination of spinning dust. emission
and thermal dust emission by more amorphous dust grains than those present in
our Galaxy.
