  We have observed the continuum emission of the interacting galaxy NGC4631 at
0.87 and 1.23mm using the Heinrich-Hertz-Telescope on Mt. Graham and the IRAM
30-m telescope on Pico Veleta. We have obtained fully sampled maps which cover
the optical emission out to a radius of about 7' at both wavelengths. For a
detailed analysis, we carefully subtracted the line contributions and
synchrotron and free-free emission from the data, which added up to 6% at
1.23mm and 10% at 0.87mm. We combined the flux densities with FIR data to
obtain dust spectra and calculate dust temperatures, absorption cross sections,
and masses. Assuming a ``standard'' dust model, which consists of two
populations of big grains at moderate and warm temperatures, we obtained
temperatures of 18K and 50K for the both components. However, such a model
suffers from an excess of the radiation at 1.23mm, and the dust absorption
cross section seems to be enhanced by a factor 3 compared to previous results
and theoretical expectations. At large galactocentric radii, where the galaxy
shows disturbances as a result of gravitational interaction, this effect seems
to be even stronger. Some possibilities to resolve these problems are
discussed. The data could be explained by a very cold dust component at a
temperature of 4-6K, an increased abundance of very small grains, or a
component of grains with unusual optical properties. We favour the latter
possibility, since the first two lead to inconsistencies.
