  We present a map of 12CO J=6-5 emission of the nuclear region of the nearby
starburst galaxy M82 at resolution 7" taken with the James Clerk Maxwell
Telescope (JCMT). This is the highest resolution map yet available at this
transition. A detailed quantitative comparison is made with emission at 12CO
J=1-0 at the same resolution yielding new insights into the excitation of
molecular gas in this galaxy. The excitation is found to be highest in the
central area of the starburst region where the ratio r_61 = 12CO J=6-5/12CO
J=1-0 is as high as 0.5, compared to the mean value over the starburst region
of 0.24. The excitation ratio peaks along the inner edge of the molecular ring
outlined by atomic and molecular gas at lower excitation, and also in two spurs
extending northward from the disk toward the outflow associated with the
supwerwind. Emission with higher than avarage excitation is also found to be
associated with the supershell surrounding the luminous SNR candidate 41.9+58,
and possibly on a larger scale in gas whose orbits are strongly influenced by
the stellar bar. The higher excitation in M82 is likely to be caused
predominantly by local increases in kinetic temperature and/or geometric
filling factor of a pre-existing higher excitation component, and less likely
to be caused by local increases in gas density.
