  Using DIRBE and FIRAS maps at high latitude ($|b|>10^{\circ}$) we derive the
spatial distribution of the dust temperature associated with the diffuse cirrus
and the dense molecular clouds. For a $\nu^2$ emissivity law, we find that the
equilibrium dust temperature of the cirrus is about 17.5 K with only small
variations over the high latitude sky. Comparison of the far Infrared DIRBE
maps shows the presence of a colder emission component with a temperature
around 15 K, assuming a $\nu^2$ emissivity law. The lowest values of the
temperature found in the cold regions ($\sim 13 K$) are compatible with the
results recently obtained for dense cores in star forming regions by the
balloon-borne experiment SPM-PRONAOS (Ristorcelli et al., 1996, 1998, Serra et
al., 1997). This cold component is in particular present in the direction of
known molecular complexes with low star forming activity such as Taurus. The
association between the cold component and molecular clouds is further
demonstrated by the fact that all sky pixels with significant cold emission
have an excess IR emission with respect to the high latitude IR/HI correlation.
We have deduced a threshold value of the column density, $N_{HI} = 2.5 10^{20}
H/cm^2$, below which cold dust is not detected within the FIRAS beam of $\sim
7\degr$. We have re-examined the problem of the existence of a very cold dust
component ($T \sim 7 K$) by combining DIRBE maps of the cold emission with
FIRAS spectra, corrected for the isotropic component found in Puget et al.
(1996). The warm and cold component deduced from the analysis of DIRBE maps
account for the Galactic FIRAS spectra with no need for a very cold component
($T\sim7$ K).
