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 H2 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. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.