  This paper presents 12CO J=3-2, 13CO J=3-2, C18O J=3-2, and 13CO J=2-1
spectra of the irregular starburst galaxy M82 taken with the 15 m James Clerk
Maxwell Telescope. All maps exhibit a double peaked morphology, despite
evidence that the higher J transitions are optically thick. This morphology
suggests that the double peaked structure is not the result of an edge-on torus
of molecular gas as is commonly assumed. We observe line ratio gradients that
can best be explained by a temperature gradient increasing from NE to SW in
conjunction with a density gradient that increases in the opposite sense. These
gradients may have been caused by the interaction with M81, resulting in
increased star formation that both heats and depletes the molecular gas in the
SW lobe of M82.
