Abstract.We have observed the continuum emission of the interacting galaxy NGC 4631 at λλ 870 µm and 1.23 mm 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 1.23 mm and 10% at 0.87 mm. 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 18 K and 50 K for the both components. However, such a model suffers from an excess of the radiation at λ 1.23 mm, 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 4-6 K, 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