We present the observations of the starburst galaxy M82 taken with the Herschel SPIRE Fourier-transform spectrometer. The spectrum (194-671 μm) 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 12CO and 13CO lines strongly indicates a very warm molecular gas component at ∼500 K and pressure of ∼3×106 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. © ESO 2010.