Using the Planck 2015 data release ( PR2 ) temperature maps , we separate Galactic thermal dust emission from cosmic infrared background ( CIB ) anisotropies . For this purpose , we implement a specifically tailored component-separation method , the so-called generalized needlet internal linear combination ( GNILC ) method , which uses spatial information ( the angular power spectra ) to disentangle the Galactic dust emission and CIB anisotropies . We produce significantly improved all-sky maps of Planck thermal dust emission , with reduced CIB contamination , at 353 , 545 , and 857 GHz . By reducing the CIB contamination of the thermal dust maps , we provide more accurate estimates of the local dust temperature and dust spectral index over the sky with reduced dispersion , especially at high Galactic latitudes above b = \pm 20 ^ { \circ } . We find that the dust temperature is T = ( 19.4 \pm 1.3 ) K and the dust spectral index is \beta = 1.6 \pm 0.1 averaged over the whole sky , while T = ( 19.4 \pm 1.5 ) K and \beta = 1.6 \pm 0.2 on 21 % of the sky at high latitudes . Moreover , subtracting the new CIB-removed thermal dust maps from the CMB-removed Planck maps gives access to the CIB anisotropies over 60 % of the sky at Galactic latitudes |b| > 20 ^ { \circ } . Because they are a significant improvement over previous Planck products , the GNILC maps are recommended for thermal dust science . The new CIB maps can be regarded as indirect tracers of the dark matter and they are recommended for exploring cross-correlations with lensing and large-scale structure optical surveys . The reconstructed GNILC thermal dust and CIB maps are delivered as Planck products .