We present high-angular-resolution, far-infrared images of the Small Magell
anic Cloud (SMC). The images were reconstructed from data obtained with the
Infrared Astronomical Satellite (IRAS), using the Pyramid Maximum Entropy
algorithm. The angular resolutions of the images are 1 arcmin at 12, 25 and
60 mu m, and 1.7 arcmin at 100 mu m, which provides an excellent complemen
t to the recent neutral hydrogen (H I) survey from the Australia Telescope
Compact Array, which has a resolution of 1.6 arcmin. We use the 60- and 100
-mu m data, together with a standard dust model, to derive a temperature ma
p and a dust column density distribution. Dust temperatures range from 23 t
o 45 K, which is, on average, warmer than for the Galaxy, although there is
a deficit of warm, very small dust grains in the SMC. The total amount of
cool dust in the SMC is 1.8(-0.2)(+1.3) x 10(4) M.. There is a significant
variation of the observed dust-to-gas ratio across the SMC. This may be cau
sed by corresponding variations in metallicity, but this explanation is not
supported by the limited available data in the literature. Alternatively,
there may be a large amount of molecular hydrogen (H-2) in the SMC, similar
to 8 x 10(8) M., and/or a large amount (similar to 10(6) M.) of cold dust
(less than or equal to 15 K) not seen by IRAS or COBE/DIRBE. The average du
st-to-atomic gas ratio is, by mass, 8.2 x 10(-5), which is a factor of simi
lar to 30 below the Galactic value. The spatial power spectrum of the dust
column density image can be approximated by P-d(k) proportional to k(-3.1),
which shows that, as with the H I power spectrum, there is no preferred sc
ale size for dust clouds. A spatial coherence analysis shows that, over a w
ide range of spatial scales (greater than or similar to 50 pc), H I and dus
t are well correlated (> 60 per cent).