The starburst galaxy M 82 has been mapped at \lambda 1.2 mm using the IRAM 30–m telescope and the MPIfR 19–channel bolometer . The influence of the sidelobe pattern and the ^ { 12 } CO ( 2 - 1 ) line has been carefully analyzed . Based on this analysis , we conclude that the cold dust does not extend far into the halo as has been previously claimed . The total mass of dust in the inner 3 kpc of the galaxy is { 7.5 \cdot 10 ^ { 6 } } M _ { \odot } . Assuming a solar gas-to-dust ratio , the inferred total mass of gas is { 7.5 \cdot 10 ^ { 8 } } M _ { \odot } . Unlike in any other galaxy we find the CO ( 2 - 1 ) line emission to be clearly more extended than the \lambda 1.2 mm dust emission . A likely explanation for this exceptional behaviour , seen for the first time in galaxies , is heating of molecular gas by low–energy cosmic rays and soft X–rays in the halo of M 82 .