We present the observations of the starburst galaxy M82 taken with the Herschel SPIRE Fourier Transform Spectrometer .
The spectrum ( 194–671 \mu m ) shows a prominent CO rotational ladder from J = 4–3 to 13–12 emitted by the central region of M82 .
The fundamental properties of the gas are well constrained by the high J lines observed for the first time .
Radiative transfer modeling of these high-S/N ^ { 12 } CO and ^ { 13 } CO lines strongly indicates a very warm molecular gas component at \sim 500 K and pressure of \sim 3 \times 10 ^ { 6 } K cm ^ { -3 } , in good agreement with the H _ { 2 } rotational lines measurements from Spitzer and ISO .
We suggest that this warm gas is heated by dissipation of turbulence in the interstellar medium ( ISM ) rather than X-rays or UV flux from the straburst .
This paper illustrates the promise of the SPIRE FTS for the study of the ISM of nearby galaxies .