We examined archival Far Ultraviolet Spectroscopic Explorer data to search for far-ultraviolet emission lines in the starburst galaxy M82. The observations were made in an outflow region that extends beyond the galactic disk. We found the O vi λ λ 1032, 1038 emission lines from the galaxy’s southern outflow region. The O vi lines suggest that the outflowing warm-hot gas is undergoing radiative cooling. We measured a radial velocity of ∼420 km s−1 from the O vi lines, which is faster than the velocity seen in Hα observations. The O vi λ1038 emission line seems to be blended with the C ii λ1037 emission line, which has a radial velocity of ∼300 km s−1, similar to what is observed in Hα observations. The outflow medium of M82 appears to be composed of gas in multiple phases with varying temperatures and kinematics. Future spectroscopic observations in high energy regimes covering a wider spatial area are necessary to understand better the properties of the warm-hot gas medium in the outflow.