Using DIRBE and FIRAS maps at high latitude (/b/ > 10 degrees) we deri
ve the spatial distribution of the dust temperature associated with th
e diffuse cirrus and the dense molecular clouds. For a nu(2) emissivit
y law, we fmd that the equilibrium dust temperature of the cirrus is a
bout 17.5 K with only small variations over the high latitude sky. Com
parison of the far Infrared DIRBE maps shows the presence of a colder
emission component with a temperature around 15 K, assuming a nu(2) em
issivity law. The lowest values of the temperature found in the cold r
egions (similar to 13 K) are compatible with the results recently obta
ined for dense cores in star forming regions by the balloon-borne expe
riment SPM-PRONAOS (Ristorcelli et al., 1996, in prep., Serra et al.,
1997). This cold component is in particular present in the direction o
f known molecular complexes with low star forming activity such as Tau
rus. The association between the cold component and molecular clouds i
s further demonstrated by the fact that all sky pixels with significan
t cold emission have an excess IR emission with respect to the high la
titude IR/HI correlation. We have deduced a threshold value of the col
umn density, N-HI=2.5 10(20) H cm(-2), below which cold dust is not de
tected within the FIRAS beam of similar to 7 degrees. We have re-exami
ned the problem of the existence of a very cold dust component (T simi
lar to 7 K) by combining DIRBE maps of the cold emission with FIRAS sp
ectra, corrected for the isotropic component found in Puget et al. (19
96). The warm and cold component deduced from the analysis of DIRBE ma
ps account for the Galactic FIRAS spectra with no need for a very cold
component (T similar to 7 K).