  We create a model for recovering the intrinsic, absorption-corrected surface
brightness distribution of a galaxy and apply the model to the M31.
  We construct a galactic model as a superposition of axially symmetric stellar
components and a dust disc to analyse the intrinsic absorption efects. Dust
column density is assumed to be proportional to the far-infrared flux of the
galaxy. Along each line of sight, the observed far-infrared spectral energy
distribution is approximated with modified black body functions considering
dust components with different temperatures, allowing to determine the
temperatures and relative column densities of the dust components.
  We apply the model to the nearby galaxy M31 using the Spitzer Space Telescope
far-infrared observations for mapping dust distribution and temperature. A warm
and a cold dust component are distinguished. The temperature of the warm dust
in M31 varies between 56 and 60 K and is highest in the spiral arms; the
temperature of the cold component is mostly 15-19 K and rises up to about 25 K
at the centre of the galaxy. The intensity-weighted mean temperature of the
dust decreases from T ~32 K at the centre to T ~20 K at R ~7 kpc and outwards.
We also calculate the intrinsic UBVRIL surface brightness distributions and the
spatial luminosity distribution. The intrinsic dust extinction in the V-colour
rises from 0.25 mag at the centre to 0.4-0.5 mag at R = 6-13 kpc and decreases
smoothly thereafter. The calculated total extinction-corrected luminosity of
M31 is L_B = (3.64 pm 0.15) 10^10L_sun, corresponding to an absolute luminosity
M_B = (-20.89 pm 0.04) mag. Of the total B-luminosity, 20% (0.24 mag) is
obscured from us by the dust inside M31. The intrinsic shape of the bulge is
slightly prolate in our best-fit model.
