We explore the implications of the hypothesis that the various phases
of the interstellar medium (ISM) in starburst galaxies are approximate
ly in pressure equilibrium, and that the heating of molecular clouds i
s due mainly to cosmic rays. This model permits the unique determinati
on of the density and temperature of the molecular gas, provided the c
osmic-ray density is known. Using two independent techniques, we estim
ate the density of cosmic rays in the starburst galaxy M82 and calcula
te the temperature and density for the molecular clouds there. The pre
dicted parameters turn out to be in good agreement with the values der
ived from various observations. The model of cosmic-ray heated molecul
ar gas is also capable of accounting for the observed temperatures of
molecular gas in the disk of our Galaxy. This suggests that, although
UV photons may well contribute to ps heating in the immediate neighbor
hood of hot stars, cosmic rays appear to be the prime source of molecu
lar cloud heating in the general ISM both for normal and for starburst
galaxies. This model predicts that the ratio I(CO)/T(v) of CO emissio
n (which is a measure of molecular cloud kinetic temperature) to nonth
ermal radio emission (which is a measure of the amount of cosmic rays
along the line of sight) is large for young star-forming regions in ga
lactic disks and small for galactic centers as compared to the average
value inferred for galactic disks (if not viewed edge-on). We argue t
hat this ratio depends on the age of a starburst region, and therefore
can be used as an age diagnostic of starbursts and galactic disk star
-forming regions. In particular, we predict that I(CO)/T(v) is larger
for younger starbursts.