We present new interferometric (12)CO (1-0) and single-dish (12)CO (3-2) observations of the central parts of D478, a large (> 200 pc) dark dust cloud located in a quiescent region of the inner disk of M31, where single-dish (12)CO (1-0) and (12)CO (2-1) observations were previously obtained. Only a small fraction (<15%) of the (12)CO (1-0) flux previously detected in this region with the single-dish telescope is recorded by the interferometer. Most of the (12)CO (1-0) emission must therefore have the appearance of a smooth surface with very little structure on scales smaller than approximate to 25 " (85 pc). Together with the earlier (12)CO (1-0) and (12)CO (2-1) single-dish results, the new (12)CO (3-2) data are in good agreement with LTE predictions for optically thick lines at T(ex) = T(kin) = 3.5 K. These results rule out the conventional model for these clouds, consisting of warm clumps with a low filling factor (as would be the case if they resembled Galactic giant molecular clouds), and confirm that large, massive, cold molecular clouds exist in the inner disk of M31 with kinetic temperatures close to that of the cosmic microwave background. Such extremely low temperatures are likely to be a consequence of the low heating rate in these particular regions of M31, where very little massive star formation is occurring at present. From the (12)CO line profile widths, we estimate the virial mass surface density of D478 to be 80-177 M(circle dot) pc(-2). This is a factor of 7-16 times larger than the value obtained by multiplying the (12)CO profile integrals with the conventional "X factor".