  Using the IRAM 30-m telescope and the 15-m JCMT, we explore the value of
para-formaldehyde (p-H_2CO) as a tracer of density and temperature of the
molecular gas in external galaxies. The target of our observations are the
lobes of the molecular ring around the center of the nearby prototypical
starburst galaxy M 82. It is shown that p-H_2CO provides one of the rare direct
molecular thermometers. Reproducing the measured line intensities with a large
velocity gradient (LVG) model, we find densities of n_H2 ~ 7 10^3 cm^-3 and
kinetic temperatures of T_kin ~ 200 K. The derived kinetic temperature is
significantly higher than the dust temperature or the temperature deduced from
ammonia (NH_3) lines, but our results agree well with the properties of the
high-excitation component seen in CO. We also present the serendipitous
discovery of the 4_2 - 3_1 line of methanol (CH_3OH) in the northeastern lobe,
which shows -- unlike CO and H_2CO -- significantly different line intensities
in the two lobes.
