- 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.