  There is growing evidence that the properties of the molecular gas in the
nuclei of starburst galaxies and in AGN may be very different from those seen
in Galactic star forming regions and that a high kinetic temperature in the
molecular gas may lead to a non-standard initial mass function in the next
generation of stars. Unfortunately, among the fundamental parameters derived
from molecular line observations, the kinetic temperature of the molecular gas
in external galaxies is often not well determined due to a lack of suitable
tracer molecules. We discuss the diagnostic power of selected transition lines
of formaldehyde (H_2CO), which can be used as a molecular thermometer as well
as an excellent tracer of the molecular gas density. As a proof of concept, we
present the results of our multi-transition line study of the H_2CO emission
from the prototypical starburst galaxy M82. Using our large velocity gradient
model, we tightly constrain the physical properties of the dense gas in the
prominent molecular lobes, completely independent of the standard "cloud
thermometer" ammonia (NH_3) or other molecular tracers. Our results agree well
with the properties of the high-excitation molecular gas component found in the
most comprehensive CO studies. Our observations also indicate that there may be
an asymmetry between the two molecular lobes.
