The warm dust (<25K) that lies in the plane of the Galaxy (scaleheight of about 0.13 kpc) was detected by IRAS and is preferentially associated with star formation regions. In this paper we describe a model of the diffuse far-infared emission from cool dust within the Galaxy. We identify a more diffuse, cool (18-22K) dust component (scaleheight of about 0.5 kpc) that has been detected by the DIRBE (at 140 and 240 μm) on the COBE satellite. This dust may be supported above the Galactic plane by radiation pressure. We show that the excess emission cannot be accounted for by the far-infrared background (upper limits of 1.0 and 0.5 MJ sr^-1 at 140 and 240mum respectively) or by the zodiacal light. The total luminosity of this cool component is ~7x10^9Lsolar, and it has a mass of ~3x10^7Msolar. We calculate extinction values for the cool component of A_v~27 mag towards the Galactic Centre, and A_v~0.3 mag at the poles.